diff --git a/distributed/client.py b/distributed/client.py
index f01eb31190..290feabd01 100644
--- a/distributed/client.py
+++ b/distributed/client.py
@@ -1502,7 +1502,17 @@ async def __aenter__(self):
 
     async def __aexit__(self, exc_type, exc_value, traceback):
         if self._previous_as_current:
-            _current_client.reset(self._previous_as_current)
+            try:
+                _current_client.reset(self._previous_as_current)
+            except ValueError as e:
+                if not e.args[0].endswith(" was created in a different Context"):
+                    raise  # pragma: nocover
+                warnings.warn(
+                    "It is deprecated to enter and exit the Client context "
+                    "manager from different tasks",
+                    DeprecationWarning,
+                    stacklevel=2,
+                )
         await self._close(
             # if we're handling an exception, we assume that it's more
             # important to deliver that exception than shutdown gracefully.
@@ -1512,7 +1522,17 @@ async def __aexit__(self, exc_type, exc_value, traceback):
 
     def __exit__(self, exc_type, exc_value, traceback):
         if self._previous_as_current:
-            _current_client.reset(self._previous_as_current)
+            try:
+                _current_client.reset(self._previous_as_current)
+            except ValueError as e:
+                if not e.args[0].endswith(" was created in a different Context"):
+                    raise  # pragma: nocover
+                warnings.warn(
+                    "It is deprecated to enter and exit the Client context "
+                    "manager from different threads",
+                    DeprecationWarning,
+                    stacklevel=2,
+                )
         self.close()
 
     def __del__(self):
diff --git a/distributed/tests/test_client.py b/distributed/tests/test_client.py
index 2ed731a160..fa60de1d88 100644
--- a/distributed/tests/test_client.py
+++ b/distributed/tests/test_client.py
@@ -1274,6 +1274,33 @@ async def client_2():
     await asyncio.gather(client_1(), client_2())
 
 
+@gen_cluster(client=False, nthreads=[])
+async def test_context_manager_used_from_different_tasks(s):
+    c = Client(s.address, asynchronous=True)
+    await asyncio.create_task(c.__aenter__())
+    with pytest.warns(
+        DeprecationWarning,
+        match=r"It is deprecated to enter and exit the Client context manager "
+        "from different tasks",
+    ):
+        await asyncio.create_task(c.__aexit__(None, None, None))
+
+
+def test_context_manager_used_from_different_threads(s, loop):
+    c = Client(s["address"])
+    with (
+        concurrent.futures.ThreadPoolExecutor(1) as tp1,
+        concurrent.futures.ThreadPoolExecutor(1) as tp2,
+    ):
+        tp1.submit(c.__enter__).result()
+        with pytest.warns(
+            DeprecationWarning,
+            match=r"It is deprecated to enter and exit the Client context manager "
+            "from different threads",
+        ):
+            tp2.submit(c.__exit__, None, None, None).result()
+
+
 def test_global_clients(loop):
     assert _get_global_client() is None
     with pytest.raises(