diff --git a/Lib/asyncio/unix_events.py b/Lib/asyncio/unix_events.py
index d8f653045ae..ef8909e47ad 100644
--- a/Lib/asyncio/unix_events.py
+++ b/Lib/asyncio/unix_events.py
@@ -460,12 +460,16 @@ class _UnixReadPipeTransport(transports.ReadTransport):
 
         self._loop.call_soon(self._protocol.connection_made, self)
         # only start reading when connection_made() has been called
-        self._loop.call_soon(self._loop._add_reader,
+        self._loop.call_soon(self._add_reader,
                              self._fileno, self._read_ready)
         if waiter is not None:
             # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(futures._set_result_unless_cancelled,
                                  waiter, None)
+    def _add_reader(self, fd, callback):
+        if not self.is_reading():
+            return
+        self._loop._add_reader(fd, callback)
 
     def __repr__(self):
         info = [self.__class__.__name__]