The England full-back was subject to interest from Bayern Munich in the summer but questioned why he would want to leave east Manchester.
"I want to stay at this club as long as possible," he said. "As they say, they will have to wheel me out! Why would I want to leave the club that has just won the Treble?
"I wanted to be settled, not just for me but for my family and now that I am, you are seeing the performances."
Walker, 33, confirmed he has been installed as one of five captains for the season after sporting the armband in the opening Premier League games.
"We are at a massive club for a reason and the hunger is still within the changing room for us to keep going. You see the manager and he does not settle for second and we want to follow in his footsteps.
"He drew a diagram at the start of the season and we are climbing the mountain again. To go again and again is what separates good teams from great teams."