diff --git a/crates/accelerate/src/sabre_layout.rs b/crates/accelerate/src/sabre_layout.rs
index 1fe1b7d53827..a2e894dd7667 100644
--- a/crates/accelerate/src/sabre_layout.rs
+++ b/crates/accelerate/src/sabre_layout.rs
@@ -41,6 +41,7 @@ pub fn sabre_layout_and_routing(
     num_swap_trials: usize,
     num_layout_trials: usize,
     seed: Option<u64>,
+    partial_layout: Option<Vec<Option<usize>>>,
 ) -> ([NLayout; 2], SwapMap, PyObject) {
     let run_in_parallel = getenv_use_multiple_threads();
     let outer_rng = match seed {
@@ -57,6 +58,7 @@ pub fn sabre_layout_and_routing(
             .into_par_iter()
             .enumerate()
             .map(|(index, seed_trial)| {
+                let partial = if index > 0 { &partial_layout } else { &None };
                 (
                     index,
                     layout_trial(
@@ -69,6 +71,7 @@ pub fn sabre_layout_and_routing(
                         max_iterations,
                         num_swap_trials,
                         run_in_parallel,
+                        partial.clone(),
                     ),
                 )
             })
@@ -83,7 +86,9 @@ pub fn sabre_layout_and_routing(
     } else {
         seed_vec
             .into_iter()
-            .map(|seed_trial| {
+            .enumerate()
+            .map(|(index, seed_trial)| {
+                let partial = if index > 0 { &partial_layout } else { &None };
                 layout_trial(
                     num_clbits,
                     &mut dag_nodes,
@@ -94,6 +99,7 @@ pub fn sabre_layout_and_routing(
                     max_iterations,
                     num_swap_trials,
                     run_in_parallel,
+                    partial.clone(),
                 )
             })
             .min_by_key(|result| result.1.map.values().map(|x| x.len()).sum::<usize>())
@@ -112,13 +118,46 @@ fn layout_trial(
     max_iterations: usize,
     num_swap_trials: usize,
     run_swap_in_parallel: bool,
+    partial_layout: Option<Vec<Option<usize>>>,
 ) -> ([NLayout; 2], SwapMap, Vec<usize>) {
     // Pick a random initial layout and fully populate ancillas in that layout too
     let num_physical_qubits = distance_matrix.shape()[0];
     let mut rng = Pcg64Mcg::seed_from_u64(seed);
-    let mut physical_qubits: Vec<usize> = (0..num_physical_qubits).collect();
-    physical_qubits.shuffle(&mut rng);
-    let mut initial_layout = NLayout::from_logical_to_physical(physical_qubits);
+    let mut physical_qubits: Vec<usize>;
+    match partial_layout {
+        Some(partial_layout_bits) => {
+            let used_bits: HashSet<usize> = partial_layout_bits
+                .iter()
+                .filter_map(|x| x.as_ref())
+                .copied()
+                .collect();
+            let mut free_bits: Vec<usize> = (0..num_physical_qubits)
+                .filter(|x| !used_bits.contains(x))
+                .collect();
+            free_bits.shuffle(&mut rng);
+            physical_qubits = partial_layout_bits
+                .iter()
+                .map(|x| match x {
+                    Some(phys) => *phys,
+                    None => free_bits.pop().unwrap(),
+                })
+                .collect();
+        }
+        None => {
+            physical_qubits = (0..num_physical_qubits).collect();
+            physical_qubits.shuffle(&mut rng);
+        }
+    };
+    let mut phys_to_logic = vec![0; num_physical_qubits];
+    physical_qubits
+        .iter()
+        .enumerate()
+        .for_each(|(logic, phys)| phys_to_logic[*phys] = logic);
+
+    let mut initial_layout = NLayout {
+        logic_to_phys: physical_qubits,
+        phys_to_logic,
+    };
     let mut rev_dag_nodes: Vec<(usize, Vec<usize>, HashSet<usize>)> =
         dag_nodes.iter().rev().cloned().collect();
     for _iter in 0..max_iterations {
diff --git a/qiskit/transpiler/passes/layout/sabre_layout.py b/qiskit/transpiler/passes/layout/sabre_layout.py
index 2702786cde3a..170a6a8f657e 100644
--- a/qiskit/transpiler/passes/layout/sabre_layout.py
+++ b/qiskit/transpiler/passes/layout/sabre_layout.py
@@ -13,8 +13,11 @@
 """Layout selection using the SABRE bidirectional search approach from Li et al.
 """
 
+from collections import defaultdict
 import copy
 import logging
+import time
+
 import numpy as np
 import rustworkx as rx
 
@@ -24,6 +27,7 @@
 from qiskit.transpiler.passes.layout.enlarge_with_ancilla import EnlargeWithAncilla
 from qiskit.transpiler.passes.layout.apply_layout import ApplyLayout
 from qiskit.transpiler.passes.layout import disjoint_utils
+from qiskit.transpiler.passes.layout import vf2_utils
 from qiskit.transpiler.passmanager import PassManager
 from qiskit.transpiler.layout import Layout
 from qiskit.transpiler.basepasses import TransformationPass
@@ -38,6 +42,8 @@
 from qiskit.transpiler.target import Target
 from qiskit.transpiler.coupling import CouplingMap
 from qiskit.tools.parallel import CPU_COUNT
+from qiskit.circuit.controlflow import ControlFlowOp, ForLoopOp
+from qiskit.converters import circuit_to_dag
 
 logger = logging.getLogger(__name__)
 
@@ -45,11 +51,16 @@
 class SabreLayout(TransformationPass):
     """Choose a Layout via iterative bidirectional routing of the input circuit.
 
-    Starting with a random initial `Layout`, the algorithm does a full routing
-    of the circuit (via the `routing_pass` method) to end up with a
-    `final_layout`. This final_layout is then used as the initial_layout for
-    routing the reverse circuit. The algorithm iterates a number of times until
-    it finds an initial_layout that reduces full routing cost.
+    The algorithm does a full routing of the circuit (via the `routing_pass`
+    method) to end up with a `final_layout`. This final_layout is then used as
+    the initial_layout for routing the reverse circuit. The algorithm iterates a
+    number of times until it finds an initial_layout that reduces full routing cost.
+
+    Prior to running the SABRE algorithm this transpiler pass will try to find the layout
+    for deepest layer that is has an isomorphic subgraph in the coupling graph. This is
+    done by progressively using the algorithm from :class:`~.VF2Layout` on the circuit
+    until a mapping is not found. This partial layout is then used to seed the SABRE algorithm
+    and then random physical bits are selected for the remaining elements in the mapping.
 
     This method exploits the reversibility of quantum circuits, and tries to
     include global circuit information in the choice of initial_layout.
@@ -85,6 +96,10 @@ def __init__(
         swap_trials=None,
         layout_trials=None,
         skip_routing=False,
+        vf2_partial_layout=True,
+        vf2_call_limit=None,
+        vf2_time_limit=None,
+        vf2_max_trials=None,
     ):
         """SabreLayout initializer.
 
@@ -121,6 +136,16 @@ def __init__(
                 will be returned in the property set. This is a tradeoff to run custom
                 routing with multiple layout trials, as using this option will cause
                 SabreLayout to run the routing stage internally but not use that result.
+            vf2_partial_layout (bool): Run vf2 partial layout
+            vf2_call_limit (int): The number of state visits to attempt in each execution of
+                VF2 to attempt to find a partial layout.
+            vf2_time_limit (float): The total time limit in seconds to run VF2 to find a partial
+                layout
+            vf2_max_trials (int): The maximum number of trials to run VF2 to find
+                a partial layout. If this is not specified the number of trials will be limited
+                based on the number of edges in the interaction graph or the coupling graph
+                (whichever is larger) if no other limits are set. If set to a value <= 0 no
+                limit on the number of trials will be set.
 
         Raises:
             TranspilerError: If both ``routing_pass`` and ``swap_trials`` or
@@ -158,6 +183,11 @@ def __init__(
                     self.coupling_map = copy.deepcopy(self.coupling_map)
                 self.coupling_map.make_symmetric()
             self._neighbor_table = NeighborTable(rx.adjacency_matrix(self.coupling_map.graph))
+        self.avg_error_map = None
+        self.vf2_partial_layout = vf2_partial_layout
+        self.call_limit = vf2_call_limit
+        self.time_limit = vf2_time_limit
+        self.max_trials = vf2_max_trials
 
     def run(self, dag):
         """Run the SabreLayout pass on `dag`.
@@ -321,6 +351,13 @@ def _inner_run(self, dag, coupling_map):
                     cargs,
                 )
             )
+        partial_layout = None
+        if self.vf2_partial_layout:
+            partial_layout_virtual_bits = self._vf2_partial_layout(
+                dag, coupling_map
+            ).get_virtual_bits()
+            partial_layout = [partial_layout_virtual_bits.get(i, None) for i in dag.qubits]
+
         ((initial_layout, final_layout), swap_map, gate_order) = sabre_layout_and_routing(
             len(dag.clbits),
             dag_list,
@@ -331,6 +368,7 @@ def _inner_run(self, dag, coupling_map):
             self.swap_trials,
             self.layout_trials,
             self.seed,
+            partial_layout,
         )
         # Apply initial layout selected.
         layout_dict = {}
@@ -385,3 +423,173 @@ def _compose_layouts(self, initial_layout, pass_final_layout, qregs):
         qubit_map = Layout.combine_into_edge_map(initial_layout, trivial_layout)
         final_layout = {v: pass_final_layout._v2p[qubit_map[v]] for v in initial_layout._v2p}
         return Layout(final_layout)
+
+    # TODO: Migrate this to rust as part of sabre_layout.rs after
+    # https://github.com/Qiskit/rustworkx/issues/741 is implemented and released
+    def _vf2_partial_layout(self, dag, coupling_map):
+        """Find a partial layout using vf2 on the deepest subgraph that is isomorphic to
+        the coupling graph."""
+        im_graph_node_map = {}
+        reverse_im_graph_node_map = {}
+        im_graph = rx.PyGraph(multigraph=False)
+        logger.debug("Buidling interaction graphs")
+        largest_im_graph = None
+        best_mapping = None
+        first_mapping = None
+        if self.avg_error_map is None:
+            self.avg_error_map = vf2_utils.build_average_error_map(self.target, None, coupling_map)
+
+        cm_graph, cm_nodes = vf2_utils.shuffle_coupling_graph(coupling_map, self.seed, False)
+        # To avoid trying to over optimize the result by default limit the number
+        # of trials based on the size of the graphs. For circuits with simple layouts
+        # like an all 1q circuit we don't want to sit forever trying every possible
+        # mapping in the search space if no other limits are set
+        if self.max_trials is None and self.call_limit is None and self.time_limit is None:
+            im_graph_edge_count = len(im_graph.edge_list())
+            cm_graph_edge_count = len(coupling_map.graph.edge_list())
+            self.max_trials = max(im_graph_edge_count, cm_graph_edge_count) + 15
+
+        start_time = time.time()
+
+        # A more efficient search pattern would be to do a binary search
+        # and find, but to conserve memory and avoid a large number of
+        # unecessary graphs this searchs from the beginning and continues
+        # until there is no vf2 match
+        def _visit(dag, weight, wire_map):
+            for node in dag.topological_op_nodes():
+                nonlocal largest_im_graph
+                largest_im_graph = im_graph.copy()
+                if getattr(node.op, "_directive", False):
+                    continue
+                if isinstance(node.op, ControlFlowOp):
+                    if isinstance(node.op, ForLoopOp):
+                        inner_weight = len(node.op.params[0]) * weight
+                    else:
+                        inner_weight = weight
+                    for block in node.op.blocks:
+                        inner_wire_map = {
+                            inner: wire_map[outer] for outer, inner in zip(node.qargs, block.qubits)
+                        }
+                        _visit(circuit_to_dag(block), inner_weight, inner_wire_map)
+                    continue
+                len_args = len(node.qargs)
+                qargs = [wire_map[q] for q in node.qargs]
+                if len_args == 1:
+                    if qargs[0] not in im_graph_node_map:
+                        weights = defaultdict(int)
+                        weights[node.name] += weight
+                        im_graph_node_map[qargs[0]] = im_graph.add_node(weights)
+                        reverse_im_graph_node_map[im_graph_node_map[qargs[0]]] = qargs[0]
+                    else:
+                        im_graph[im_graph_node_map[qargs[0]]][node.op.name] += weight
+                if len_args == 2:
+                    if qargs[0] not in im_graph_node_map:
+                        im_graph_node_map[qargs[0]] = im_graph.add_node(defaultdict(int))
+                        reverse_im_graph_node_map[im_graph_node_map[qargs[0]]] = qargs[0]
+                    if qargs[1] not in im_graph_node_map:
+                        im_graph_node_map[qargs[1]] = im_graph.add_node(defaultdict(int))
+                        reverse_im_graph_node_map[im_graph_node_map[qargs[1]]] = qargs[1]
+                    edge = (im_graph_node_map[qargs[0]], im_graph_node_map[qargs[1]])
+                    if im_graph.has_edge(*edge):
+                        im_graph.get_edge_data(*edge)[node.name] += weight
+                    else:
+                        weights = defaultdict(int)
+                        weights[node.name] += weight
+                        im_graph.add_edge(*edge, weights)
+                if len_args > 2:
+                    raise TranspilerError(
+                        "Encountered an instruction operating on more than 2 qubits, this pass "
+                        "only functions with 1 or 2 qubit operations."
+                    )
+                vf2_mapping = rx.vf2_mapping(
+                    cm_graph,
+                    im_graph,
+                    subgraph=True,
+                    id_order=False,
+                    induced=False,
+                    call_limit=self.call_limit,
+                )
+                try:
+                    nonlocal first_mapping
+                    first_mapping = next(vf2_mapping)
+                except StopIteration:
+                    break
+                nonlocal best_mapping
+                best_mapping = vf2_mapping
+                elapsed_time = time.time() - start_time
+                if (
+                    self.time_limit is not None
+                    and best_mapping is not None
+                    and elapsed_time >= self.time_limit
+                ):
+                    logger.debug(
+                        "SabreLayout VF2 heuristic has taken %s which exceeds configured max time: %s",
+                        elapsed_time,
+                        self.time_limit,
+                    )
+                    break
+
+        _visit(dag, 1, {bit: bit for bit in dag.qubits})
+        logger.debug("Finding best mappings of largest partial subgraph")
+        im_graph = largest_im_graph
+
+        def mapping_to_layout(layout_mapping):
+            return Layout({reverse_im_graph_node_map[k]: v for k, v in layout_mapping.items()})
+
+        layout_mapping = {im_i: cm_nodes[cm_i] for cm_i, im_i in first_mapping.items()}
+        chosen_layout = mapping_to_layout(layout_mapping)
+        chosen_layout_score = vf2_utils.score_layout(
+            self.avg_error_map,
+            layout_mapping,
+            im_graph_node_map,
+            reverse_im_graph_node_map,
+            im_graph,
+            False,
+        )
+        trials = 1
+        for mapping in best_mapping:  # pylint: disable=not-an-iterable
+            trials += 1
+            logger.debug("Running trial: %s", trials)
+            layout_mapping = {im_i: cm_nodes[cm_i] for cm_i, im_i in mapping.items()}
+            # If the graphs have the same number of nodes we don't need to score or do multiple
+            # trials as the score heuristic currently doesn't weigh nodes based on gates on a
+            # qubit so the scores will always all be the same
+            if len(cm_graph) == len(im_graph):
+                break
+            layout_score = vf2_utils.score_layout(
+                self.avg_error_map,
+                layout_mapping,
+                im_graph_node_map,
+                reverse_im_graph_node_map,
+                im_graph,
+                False,
+            )
+            logger.debug("Trial %s has score %s", trials, layout_score)
+            if chosen_layout is None:
+                chosen_layout = mapping_to_layout(layout_mapping)
+                chosen_layout_score = layout_score
+            elif layout_score < chosen_layout_score:
+                layout = mapping_to_layout(layout_mapping)
+                logger.debug(
+                    "Found layout %s has a lower score (%s) than previous best %s (%s)",
+                    layout,
+                    layout_score,
+                    chosen_layout,
+                    chosen_layout_score,
+                )
+                chosen_layout = layout
+                chosen_layout_score = layout_score
+            if self.max_trials and trials >= self.max_trials:
+                logger.debug("Trial %s is >= configured max trials %s", trials, self.max_trials)
+                break
+            elapsed_time = time.time() - start_time
+            if self.time_limit is not None and elapsed_time >= self.time_limit:
+                logger.debug(
+                    "VF2Layout has taken %s which exceeds configured max time: %s",
+                    elapsed_time,
+                    self.time_limit,
+                )
+                break
+        for reg in dag.qregs.values():
+            chosen_layout.add_register(reg)
+        return chosen_layout
diff --git a/qiskit/transpiler/preset_passmanagers/level1.py b/qiskit/transpiler/preset_passmanagers/level1.py
index db8b09b716b0..fb8f35bedb6e 100644
--- a/qiskit/transpiler/preset_passmanagers/level1.py
+++ b/qiskit/transpiler/preset_passmanagers/level1.py
@@ -156,6 +156,7 @@ def _vf2_match_not_found(property_set):
             layout_trials=5,
             skip_routing=pass_manager_config.routing_method is not None
             and routing_method != "sabre",
+            vf2_call_limit=int(5e4),
         )
     elif layout_method is None:
         _improve_layout = common.if_has_control_flow_else(
@@ -168,6 +169,7 @@ def _vf2_match_not_found(property_set):
                 layout_trials=5,
                 skip_routing=pass_manager_config.routing_method is not None
                 and routing_method != "sabre",
+                vf2_call_limit=int(5e4),
             ),
         ).to_flow_controller()
 
diff --git a/qiskit/transpiler/preset_passmanagers/level2.py b/qiskit/transpiler/preset_passmanagers/level2.py
index 743018881da3..e2b609682894 100644
--- a/qiskit/transpiler/preset_passmanagers/level2.py
+++ b/qiskit/transpiler/preset_passmanagers/level2.py
@@ -146,6 +146,7 @@ def _vf2_match_not_found(property_set):
             layout_trials=10,
             skip_routing=pass_manager_config.routing_method is not None
             and routing_method != "sabre",
+            vf2_call_limit=int(5e6),
         )
 
     # Choose routing pass
diff --git a/qiskit/transpiler/preset_passmanagers/level3.py b/qiskit/transpiler/preset_passmanagers/level3.py
index 7fe64eed521d..8f373618d683 100644
--- a/qiskit/transpiler/preset_passmanagers/level3.py
+++ b/qiskit/transpiler/preset_passmanagers/level3.py
@@ -152,6 +152,7 @@ def _vf2_match_not_found(property_set):
             layout_trials=20,
             skip_routing=pass_manager_config.routing_method is not None
             and routing_method != "sabre",
+            vf2_call_limit=int(3e7),
         )
 
     # Choose routing pass