diff --git a/fsspec/generic.py b/fsspec/generic.py
index 18e27405a..869047746 100644
--- a/fsspec/generic.py
+++ b/fsspec/generic.py
@@ -280,9 +280,11 @@ async def _cp_file(
                 if hasattr(fs2, "open_async")
                 else fs2.open(url2, "wb", **kw)
             )
-            while f1.size is None or f2.tell() < f1.size:
+            while await maybe_await(f1.size) is None or f2.tell() < await maybe_await(
+                f1.size
+            ):
                 data = await maybe_await(f1.read(blocksize))
-                if f1.size is None and not data:
+                if await maybe_await(f1.size) is None and not data:
                     break
                 await maybe_await(f2.write(data))
                 callback.absolute_update(f2.tell())