diff --git a/telethon/extensions/tcp_client.py b/telethon/extensions/tcp_client.py
index 9a37c685..8453af5e 100644
--- a/telethon/extensions/tcp_client.py
+++ b/telethon/extensions/tcp_client.py
@@ -3,12 +3,15 @@ import errno
 import socket
 from datetime import timedelta
 from io import BytesIO, BufferedWriter
+from threading import Lock
 
 
 class TcpClient:
     def __init__(self, proxy=None, timeout=timedelta(seconds=5)):
         self._proxy = proxy
         self._socket = None
+        self._closing_lock = Lock()
+
         if isinstance(timeout, timedelta):
             self._timeout = timeout.seconds
         elif isinstance(timeout, int) or isinstance(timeout, float):
@@ -48,14 +51,19 @@ class TcpClient:
 
     def close(self):
         """Closes the connection"""
-        try:
-            if self.connected:
-                self._socket.shutdown(socket.SHUT_RDWR)
-                self._socket.close()
-        except OSError:
-            pass  # Ignore ENOTCONN, EBADF, and any other error when closing
-        finally:
-            self._socket = None
+        if self._closing_lock.locked():
+            # Already closing, no need to close again (avoid None.close())
+            return
+
+        with self._closing_lock:
+            try:
+                if self._socket is not None:
+                    self._socket.shutdown(socket.SHUT_RDWR)
+                    self._socket.close()
+            except OSError:
+                pass  # Ignore ENOTCONN, EBADF, and any other error when closing
+            finally:
+                self._socket = None
 
     def write(self, data):
         """Writes (sends) the specified bytes to the connected peer"""