diff --git a/qiskit/transpiler/passes/layout/vf2_post_layout.py b/qiskit/transpiler/passes/layout/vf2_post_layout.py
index 1e874affa7c9..19570d6c4908 100644
--- a/qiskit/transpiler/passes/layout/vf2_post_layout.py
+++ b/qiskit/transpiler/passes/layout/vf2_post_layout.py
@@ -106,6 +106,7 @@ def __init__(
         call_limit=None,
         time_limit=None,
         strict_direction=True,
+        max_trials=0,
     ):
         """Initialize a ``VF2PostLayout`` pass instance
 
@@ -131,6 +132,8 @@ def __init__(
                 However, if ``strict_direction=True`` the pass expects the input
                 :class:`~.DAGCircuit` object to :meth:`~.VF2PostLayout.run` to be in
                 the target set of instructions.
+            max_trials (int): The maximum number of trials to run VF2 to find
+                a layout. A value of ``0`` (the default) means 'unlimited'.
 
         Raises:
             TypeError: At runtime, if neither ``coupling_map`` or ``target`` are provided.
@@ -141,6 +144,7 @@ def __init__(
         self.properties = properties
         self.call_limit = call_limit
         self.time_limit = time_limit
+        self.max_trials = max_trials
         self.seed = seed
         self.strict_direction = strict_direction
         self.avg_error_map = None
@@ -310,6 +314,11 @@ def run(self, dag):
                 )
                 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(
diff --git a/releasenotes/notes/vf2-post-layout-max-trials-98b1c736e2e33861.yaml b/releasenotes/notes/vf2-post-layout-max-trials-98b1c736e2e33861.yaml
new file mode 100644
index 000000000000..c4c047871de4
--- /dev/null
+++ b/releasenotes/notes/vf2-post-layout-max-trials-98b1c736e2e33861.yaml
@@ -0,0 +1,12 @@
+---
+features:
+  - |
+    Added a new parameter ``max_trials`` to pass :class:`~.VF2PostLayout`
+    which, when specified, limits the number of layouts discovered and
+    compared when searching for the best layout.
+    This differs from existing parameters ``call_limit`` and ``time_limit``
+    (which are used to limit the number of state visits performed by the VF2
+    algorithm and the total time spent by pass :class:`~.VF2PostLayout`,
+    respectively) in that it is used to place an upper bound on the time
+    spent scoring potential layouts, which may be useful for larger
+    devices.
diff --git a/test/python/transpiler/test_vf2_post_layout.py b/test/python/transpiler/test_vf2_post_layout.py
index 9b48ecbb445e..d06e46a229bd 100644
--- a/test/python/transpiler/test_vf2_post_layout.py
+++ b/test/python/transpiler/test_vf2_post_layout.py
@@ -239,6 +239,39 @@ def test_2q_circuit_5q_backend_controlflow(self):
         self.assertLayout(dag, cmap, pass_.property_set)
         self.assertNotEqual(pass_.property_set["post_layout"], initial_layout)
 
+    def test_2q_circuit_5q_backend_max_trials(self):
+        """A simple example, without considering the direction
+          0 - 1
+        qr1 - qr0
+        """
+        max_trials = 11
+        backend = FakeYorktown()
+
+        qr = QuantumRegister(2, "qr")
+        circuit = QuantumCircuit(qr)
+        circuit.cx(qr[1], qr[0])  # qr1 -> qr0
+        tqc = transpile(circuit, backend, layout_method="dense")
+        initial_layout = tqc._layout
+        dag = circuit_to_dag(tqc)
+        cmap = CouplingMap(backend.configuration().coupling_map)
+        props = backend.properties()
+        pass_ = VF2PostLayout(
+            coupling_map=cmap, properties=props, seed=self.seed, max_trials=max_trials
+        )
+
+        with self.assertLogs(
+            "qiskit.transpiler.passes.layout.vf2_post_layout", level="DEBUG"
+        ) as cm:
+            pass_.run(dag)
+        self.assertIn(
+            f"DEBUG:qiskit.transpiler.passes.layout.vf2_post_layout:Trial {max_trials} "
+            f"is >= configured max trials {max_trials}",
+            cm.output,
+        )
+
+        self.assertLayout(dag, cmap, pass_.property_set)
+        self.assertNotEqual(pass_.property_set["post_layout"], initial_layout)
+
     def test_best_mapping_ghz_state_full_device_multiple_qregs_v2(self):
         """Test best mappings with multiple registers"""
         backend = FakeLimaV2()