diff --git a/CHANGES/8967.bugfix.rst b/CHANGES/8967.bugfix.rst
new file mode 100644
index 00000000000..1046f36bd8b
--- /dev/null
+++ b/CHANGES/8967.bugfix.rst
@@ -0,0 +1 @@
+Fixed resolve_host() 'Task was destroyed but is pending' errors -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/connector.py b/aiohttp/connector.py
index d9b3471259d..261cd28e12b 100644
--- a/aiohttp/connector.py
+++ b/aiohttp/connector.py
@@ -14,7 +14,7 @@
 from itertools import cycle, islice
 from time import monotonic
 from types import TracebackType
-from typing import (  # noqa
+from typing import (
     TYPE_CHECKING,
     Any,
     Awaitable,
@@ -404,8 +404,8 @@ async def close(self) -> None:
                     err_msg = "Error while closing connector: " + repr(res)
                     logging.error(err_msg)
 
-    def _close_immediately(self) -> List["asyncio.Future[None]"]:
-        waiters: List["asyncio.Future[None]"] = []
+    def _close_immediately(self) -> List[Awaitable[object]]:
+        waiters: List[Awaitable[object]] = []
 
         if self._closed:
             return waiters
@@ -805,11 +805,19 @@ def __init__(
         self._local_addr_infos = aiohappyeyeballs.addr_to_addr_infos(local_addr)
         self._happy_eyeballs_delay = happy_eyeballs_delay
         self._interleave = interleave
+        self._resolve_host_tasks: Set["asyncio.Task[List[ResolveResult]]"] = set()
 
-    def _close_immediately(self) -> List["asyncio.Future[None]"]:
+    def _close_immediately(self) -> List[Awaitable[object]]:
         for ev in self._throttle_dns_events.values():
             ev.cancel()
-        return super()._close_immediately()
+
+        waiters = super()._close_immediately()
+
+        for t in self._resolve_host_tasks:
+            t.cancel()
+            waiters.append(t)
+
+        return waiters
 
     @property
     def family(self) -> int:
@@ -885,6 +893,8 @@ async def _resolve_host(
         resolved_host_task = asyncio.create_task(
             self._resolve_host_with_throttle(key, host, port, traces)
         )
+        self._resolve_host_tasks.add(resolved_host_task)
+        resolved_host_task.add_done_callback(self._resolve_host_tasks.discard)
         try:
             return await asyncio.shield(resolved_host_task)
         except asyncio.CancelledError:
diff --git a/tests/test_connector.py b/tests/test_connector.py
index ea30e571b95..d66bc214ed2 100644
--- a/tests/test_connector.py
+++ b/tests/test_connector.py
@@ -9,7 +9,7 @@
 import sys
 import uuid
 from collections import deque
-from contextlib import closing
+from contextlib import closing, suppress
 from typing import (
     Awaitable,
     Callable,
@@ -1839,6 +1839,39 @@ async def test_close_cancels_cleanup_handle(
     assert conn._cleanup_handle is None
 
 
+async def test_close_cancels_resolve_host(loop: asyncio.AbstractEventLoop) -> None:
+    cancelled = False
+
+    async def delay_resolve_host(*args: object) -> None:
+        """Delay _resolve_host() task in order to test cancellation."""
+        nonlocal cancelled
+        try:
+            await asyncio.sleep(10)
+        except asyncio.CancelledError:
+            cancelled = True
+            raise
+
+    conn = aiohttp.TCPConnector()
+    req = ClientRequest(
+        "GET", URL("http://localhost:80"), loop=loop, response_class=mock.Mock()
+    )
+    with mock.patch.object(conn, "_resolve_host_with_throttle", delay_resolve_host):
+        t = asyncio.create_task(conn.connect(req, [], ClientTimeout()))
+        # Let it create the internal task
+        await asyncio.sleep(0)
+        # Let that task start running
+        await asyncio.sleep(0)
+
+        # We now have a task being tracked and can ensure that .close() cancels it.
+        assert len(conn._resolve_host_tasks) == 1
+        await conn.close()
+        assert cancelled
+        assert len(conn._resolve_host_tasks) == 0
+
+        with suppress(asyncio.CancelledError):
+            await t
+
+
 async def test_close_abort_closed_transports(loop: asyncio.AbstractEventLoop) -> None:
     tr = mock.Mock()