diff --git a/distributed/deploy/spec.py b/distributed/deploy/spec.py
index 49d51490d7..82ba4e6607 100644
--- a/distributed/deploy/spec.py
+++ b/distributed/deploy/spec.py
@@ -355,7 +355,10 @@ async def _correct_state_internal(self) -> None:
 
             to_close = set(self.workers) - set(self.worker_spec)
             if to_close:
-                if self.scheduler.status == Status.running:
+                if (
+                    self.scheduler.status == Status.running
+                    and self.status != Status.closing
+                ):
                     await self.scheduler_comm.retire_workers(workers=list(to_close))
                 tasks = [
                     asyncio.create_task(self.workers[w].close())
diff --git a/distributed/deploy/tests/test_spec_cluster.py b/distributed/deploy/tests/test_spec_cluster.py
index ab1ec27e31..7aa3d987fb 100644
--- a/distributed/deploy/tests/test_spec_cluster.py
+++ b/distributed/deploy/tests/test_spec_cluster.py
@@ -511,6 +511,42 @@ async def test_bad_close():
     assert not record
 
 
+@gen_test()
+async def test_correct_state_skips_retirement_while_closing():
+    retired = False
+
+    class DummyScheduler:
+        status = Status.running
+
+    class DummySchedulerComm:
+        async def retire_workers(self, workers):
+            nonlocal retired
+            retired = True
+
+    class DummyWorker:
+        def __init__(self):
+            self.closed = False
+
+        async def close(self):
+            self.closed = True
+
+    cluster = object.__new__(SpecCluster)
+    cluster._lock = asyncio.Lock()
+    cluster._correct_state_waiting = None
+    cluster.status = Status.closing
+    cluster.scheduler = DummyScheduler()
+    cluster.scheduler_comm = DummySchedulerComm()
+    worker = DummyWorker()
+    cluster.workers = {"worker": worker}
+    cluster.worker_spec = {}
+
+    await cluster._correct_state_internal()
+
+    assert not retired
+    assert worker.closed
+    assert not cluster.workers
+
+
 @gen_test()
 async def test_shutdown_scheduler_disabled():
     async with SpecCluster(