diff --git a/discord/client.py b/discord/client.py
index b3243ef93..f452ca30a 100644
--- a/discord/client.py
+++ b/discord/client.py
@@ -287,7 +287,7 @@ class Client:
         self._enable_debug_events: bool = options.pop('enable_debug_events', False)
         self._connection: ConnectionState[Self] = self._get_state(intents=intents, **options)
         self._connection.shard_count = self.shard_count
-        self._closed: bool = False
+        self._closing_task: Optional[asyncio.Task[None]] = None
         self._ready: asyncio.Event = MISSING
         self._application: Optional[AppInfo] = None
         self._connection._get_websocket = self._get_websocket
@@ -307,7 +307,10 @@ class Client:
         exc_value: Optional[BaseException],
         traceback: Optional[TracebackType],
     ) -> None:
-        if not self.is_closed():
+        # This avoids double-calling a user-provided .close()
+        if self._closing_task:
+            await self._closing_task
+        else:
             await self.close()
 
     # internals
@@ -726,22 +729,24 @@ class Client:
 
         Closes the connection to Discord.
         """
-        if self._closed:
-            return
+        if self._closing_task:
+            return await self._closing_task
 
-        self._closed = True
+        async def _close():
+            await self._connection.close()
 
-        await self._connection.close()
+            if self.ws is not None and self.ws.open:
+                await self.ws.close(code=1000)
 
-        if self.ws is not None and self.ws.open:
-            await self.ws.close(code=1000)
+            await self.http.close()
 
-        await self.http.close()
+            if self._ready is not MISSING:
+                self._ready.clear()
 
-        if self._ready is not MISSING:
-            self._ready.clear()
+            self.loop = MISSING
 
-        self.loop = MISSING
+        self._closing_task = asyncio.create_task(_close())
+        await self._closing_task
 
     def clear(self) -> None:
         """Clears the internal state of the bot.
@@ -750,7 +755,7 @@ class Client:
         and :meth:`is_ready` both return ``False`` along with the bot's internal
         cache cleared.
         """
-        self._closed = False
+        self._closing_task = None
         self._ready.clear()
         self._connection.clear()
         self.http.clear()
@@ -870,7 +875,7 @@ class Client:
 
     def is_closed(self) -> bool:
         """:class:`bool`: Indicates if the websocket connection is closed."""
-        return self._closed
+        return self._closing_task is not None
 
     @property
     def activity(self) -> Optional[ActivityTypes]:
diff --git a/discord/shard.py b/discord/shard.py
index fc8e3380a..52155aa24 100644
--- a/discord/shard.py
+++ b/discord/shard.py
@@ -481,18 +481,21 @@ class AutoShardedClient(Client):
 
         Closes the connection to Discord.
         """
-        if self.is_closed():
-            return
+        if self._closing_task:
+            return await self._closing_task
+
+        async def _close():
+            await self._connection.close()
 
-        self._closed = True
-        await self._connection.close()
+            to_close = [asyncio.ensure_future(shard.close(), loop=self.loop) for shard in self.__shards.values()]
+            if to_close:
+                await asyncio.wait(to_close)
 
-        to_close = [asyncio.ensure_future(shard.close(), loop=self.loop) for shard in self.__shards.values()]
-        if to_close:
-            await asyncio.wait(to_close)
+            await self.http.close()
+            self.__queue.put_nowait(EventItem(EventType.clean_close, None, None))
 
-        await self.http.close()
-        self.__queue.put_nowait(EventItem(EventType.clean_close, None, None))
+        self._closing_task = asyncio.create_task(_close())
+        await self._closing_task
 
     async def change_presence(
         self,