diff --git a/sniffio/_impl.py b/sniffio/_impl.py
index 015f493..c11a157 100644
--- a/sniffio/_impl.py
+++ b/sniffio/_impl.py
@@ -65,10 +65,6 @@ async def generic_sleep(seconds):
             current_task = asyncio.Task.current_task  # type: ignore[attr-defined]
         try:
             if current_task() is not None:
-                if (3, 7) <= sys.version_info:
-                    # asyncio has contextvars support, and we're in a task, so
-                    # we can safely cache the sniffed value
-                    current_async_library_cvar.set("asyncio")
                 return "asyncio"
         except RuntimeError:
             pass