diff --git a/src/prefect/utilities/processutils.py b/src/prefect/utilities/processutils.py
index 46729b5c59b2..c17250256b5e 100644
--- a/src/prefect/utilities/processutils.py
+++ b/src/prefect/utilities/processutils.py
@@ -8,7 +8,7 @@
 import anyio.abc
 from anyio.streams.text import TextReceiveStream, TextSendStream
 
-TextSink = Union[TextIO, TextSendStream]
+TextSink = Union[anyio.AsyncFile, TextIO, TextSendStream]
 
 
 @asynccontextmanager
@@ -101,9 +101,17 @@ async def consume_process_output(
 
 
 async def stream_text(source: TextReceiveStream, sink: Optional[TextSink]):
+    if isinstance(sink, TextIOBase):
+        # Convert the blocking sink to an async-compatible object
+        sink = anyio.wrap_file(sink)
+
     async for item in source:
         if isinstance(sink, TextSendStream):
             await sink.send(item)
-        elif isinstance(sink, TextIOBase):
-            sink.write(item)
-            sink.flush()
+        elif isinstance(sink, anyio.AsyncFile):
+            await sink.write(item)
+            await sink.flush()
+        elif sink is None:
+            pass  # Consume the item but perform no action
+        else:
+            raise TypeError(f"Unsupported sink type {type(sink).__name__}")