diff --git a/asyncpg/compat.py b/asyncpg/compat.py
index 435b4c48..881873a2 100644
--- a/asyncpg/compat.py
+++ b/asyncpg/compat.py
@@ -52,6 +52,13 @@ async def wait_closed(stream: asyncio.StreamWriter) -> None:
             pass
 
 
+if sys.version_info < (3, 12):
+    def markcoroutinefunction(c):  # type: ignore
+        pass
+else:
+    from inspect import markcoroutinefunction  # noqa: F401
+
+
 if sys.version_info < (3, 12):
     from ._asyncio_compat import wait_for as wait_for  # noqa: F401
 else:
diff --git a/asyncpg/pool.py b/asyncpg/pool.py
index 06e698df..7b588c27 100644
--- a/asyncpg/pool.py
+++ b/asyncpg/pool.py
@@ -33,7 +33,8 @@ def __new__(mcls, name, bases, dct, *, wrap=False):
                 if not inspect.isfunction(meth):
                     continue
 
-                wrapper = mcls._wrap_connection_method(attrname)
+                iscoroutine = inspect.iscoroutinefunction(meth)
+                wrapper = mcls._wrap_connection_method(attrname, iscoroutine)
                 wrapper = functools.update_wrapper(wrapper, meth)
                 dct[attrname] = wrapper
 
@@ -43,7 +44,7 @@ def __new__(mcls, name, bases, dct, *, wrap=False):
         return super().__new__(mcls, name, bases, dct)
 
     @staticmethod
-    def _wrap_connection_method(meth_name):
+    def _wrap_connection_method(meth_name, iscoroutine):
         def call_con_method(self, *args, **kwargs):
             # This method will be owned by PoolConnectionProxy class.
             if self._con is None:
@@ -55,6 +56,9 @@ def call_con_method(self, *args, **kwargs):
             meth = getattr(self._con.__class__, meth_name)
             return meth(self._con, *args, **kwargs)
 
+        if iscoroutine:
+            compat.markcoroutinefunction(call_con_method)
+
         return call_con_method