diff --git a/homeassistant/core.py b/homeassistant/core.py
index 8e88820bf70..b2a00cce038 100644
--- a/homeassistant/core.py
+++ b/homeassistant/core.py
@@ -82,7 +82,11 @@ from .exceptions import (
 from .helpers.aiohttp_compat import restore_original_aiohttp_cancel_behavior
 from .helpers.json import json_dumps
 from .util import dt as dt_util, location, ulid as ulid_util
-from .util.async_ import run_callback_threadsafe, shutdown_run_callback_threadsafe
+from .util.async_ import (
+    cancelling,
+    run_callback_threadsafe,
+    shutdown_run_callback_threadsafe,
+)
 from .util.read_only_dict import ReadOnlyDict
 from .util.timeout import TimeoutManager
 from .util.unit_system import (
@@ -678,7 +682,11 @@ class HomeAssistant:
         start_time: float | None = None
         current_task = asyncio.current_task()
 
-        while tasks := [task for task in self._tasks if task is not current_task]:
+        while tasks := [
+            task
+            for task in self._tasks
+            if task is not current_task and not cancelling(task)
+        ]:
             await self._await_and_log_pending(tasks)
 
             if start_time is None:
@@ -791,7 +799,7 @@ class HomeAssistant:
         # while we are awaiting canceled tasks to get their result
         # which will result in the set size changing during iteration
         for task in list(running_tasks):
-            if task.done():
+            if task.done() or cancelling(task):
                 # Since we made a copy we need to check
                 # to see if the task finished while we
                 # were awaiting another task
diff --git a/homeassistant/util/async_.py b/homeassistant/util/async_.py
index 5b119a58c22..4caf074b879 100644
--- a/homeassistant/util/async_.py
+++ b/homeassistant/util/async_.py
@@ -1,7 +1,7 @@
 """Asyncio utilities."""
 from __future__ import annotations
 
-from asyncio import Semaphore, gather, get_running_loop
+from asyncio import Future, Semaphore, gather, get_running_loop
 from asyncio.events import AbstractEventLoop
 from collections.abc import Awaitable, Callable
 import concurrent.futures
@@ -20,6 +20,13 @@ _R = TypeVar("_R")
 _P = ParamSpec("_P")
 
 
+def cancelling(task: Future[Any]) -> bool:
+    """Return True if task is done or cancelling."""
+    # https://docs.python.org/3/library/asyncio-task.html#asyncio.Task.cancelling
+    # is new in Python 3.11
+    return bool((cancelling_ := getattr(task, "cancelling", None)) and cancelling_())
+
+
 def run_callback_threadsafe(
     loop: AbstractEventLoop, callback: Callable[..., _T], *args: Any
 ) -> concurrent.futures.Future[_T]: