diff --git a/vllm/engine/async_llm_engine.py b/vllm/engine/async_llm_engine.py
index 9f72a0d11974f..37a2dc77a3b50 100644
--- a/vllm/engine/async_llm_engine.py
+++ b/vllm/engine/async_llm_engine.py
@@ -1,8 +1,8 @@
 import asyncio
 import time
 from functools import partial
-from typing import (Any, AsyncIterator, Callable, Dict, Iterable, List,
-                    Optional, Set, Tuple, Type, Union)
+from typing import (AsyncIterator, Callable, Dict, Iterable, List, Optional,
+                    Set, Tuple, Type, Union)
 
 from transformers import PreTrainedTokenizer
 
@@ -327,7 +327,7 @@ def __init__(self,
         # We need to keep a reference to unshielded
         # task as well to prevent it from being garbage
         # collected
-        self._background_loop_unshielded: Optional[asyncio.Task[Any]] = None
+        self._background_loop_unshielded: Optional[asyncio.Task] = None
         self.start_engine_loop = start_engine_loop
         self._errored_with: Optional[BaseException] = None
 
diff --git a/vllm/entrypoints/openai/api_server.py b/vllm/entrypoints/openai/api_server.py
index f9e294af47253..44a946f2e32d4 100644
--- a/vllm/entrypoints/openai/api_server.py
+++ b/vllm/entrypoints/openai/api_server.py
@@ -4,7 +4,7 @@
 import re
 from contextlib import asynccontextmanager
 from http import HTTPStatus
-from typing import Any, Set
+from typing import Set
 
 import fastapi
 import uvicorn
@@ -34,7 +34,7 @@
 openai_serving_completion: OpenAIServingCompletion
 logger = init_logger(__name__)
 
-_running_tasks: Set[asyncio.Task[Any]] = set()
+_running_tasks: Set[asyncio.Task] = set()
 
 
 @asynccontextmanager