diff --git a/homeassistant/components/esphome/bluetooth/client.py b/homeassistant/components/esphome/bluetooth/client.py
index 00b9883f261..f7c9da48883 100644
--- a/homeassistant/components/esphome/bluetooth/client.py
+++ b/homeassistant/components/esphome/bluetooth/client.py
@@ -4,6 +4,7 @@ from __future__ import annotations
 import asyncio
 from collections.abc import Callable, Coroutine
 import contextlib
+from functools import partial
 import logging
 from typing import Any, TypeVar, cast
 import uuid
@@ -56,38 +57,40 @@ def mac_to_int(address: str) -> int:
     return int(address.replace(":", ""), 16)
 
 
+def _on_disconnected(task: asyncio.Task[Any], _: asyncio.Future[None]) -> None:
+    if task and not task.done():
+        task.cancel()
+
+
 def verify_connected(func: _WrapFuncType) -> _WrapFuncType:
     """Define a wrapper throw BleakError if not connected."""
 
     async def _async_wrap_bluetooth_connected_operation(
         self: ESPHomeClient, *args: Any, **kwargs: Any
     ) -> Any:
-        loop = self._loop  # pylint: disable=protected-access
-        disconnected_futures = (
-            self._disconnected_futures  # pylint: disable=protected-access
-        )
+        # pylint: disable=protected-access
+        loop = self._loop
+        disconnected_futures = self._disconnected_futures
         disconnected_future = loop.create_future()
+        disconnect_handler = partial(_on_disconnected, asyncio.current_task(loop))
+        disconnected_future.add_done_callback(disconnect_handler)
         disconnected_futures.add(disconnected_future)
-
-        task = asyncio.current_task(loop)
-
-        def _on_disconnected(fut: asyncio.Future[None]) -> None:
-            if task and not task.done():
-                task.cancel()
-
-        disconnected_future.add_done_callback(_on_disconnected)
         try:
             return await func(self, *args, **kwargs)
         except asyncio.CancelledError as ex:
-            source_name = self._source_name  # pylint: disable=protected-access
-            ble_device = self._ble_device  # pylint: disable=protected-access
+            if not disconnected_future.done():
+                # If the disconnected future is not done, the task was cancelled
+                # externally and we need to raise cancelled error to avoid
+                # blocking the cancellation.
+                raise
+            ble_device = self._ble_device
             raise BleakError(
-                f"{source_name}: {ble_device.name} - {ble_device.address}: "
+                f"{self._source_name }: {ble_device.name} - {ble_device.address}: "
                 "Disconnected during operation"
             ) from ex
         finally:
             disconnected_futures.discard(disconnected_future)
-            disconnected_future.remove_done_callback(_on_disconnected)
+            disconnected_future.remove_done_callback(disconnect_handler)
 
     return cast(_WrapFuncType, _async_wrap_bluetooth_connected_operation)