diff --git a/src/socketio/async_client.py b/src/socketio/async_client.py
index 0d85aa1..fb1abc1 100644
--- a/src/socketio/async_client.py
+++ b/src/socketio/async_client.py
@@ -581,7 +581,7 @@ class AsyncClient(base_client.BaseClient):
         self.callbacks = {}
         self._binary_packet = None
         self.sid = None
-        if will_reconnect:
+        if will_reconnect and not self._reconnect_task:
             self._reconnect_task = self.start_background_task(
                 self._handle_reconnect)
 
diff --git a/src/socketio/client.py b/src/socketio/client.py
index 00d7961..c4f9eaa 100644
--- a/src/socketio/client.py
+++ b/src/socketio/client.py
@@ -539,7 +539,7 @@ class Client(base_client.BaseClient):
         self.callbacks = {}
         self._binary_packet = None
         self.sid = None
-        if will_reconnect:
+        if will_reconnect and not self._reconnect_task:
             self._reconnect_task = self.start_background_task(
                 self._handle_reconnect)