Arsenal have also previously been linked but the Nerazzurri captain says he has absolutely no intentions of leaving Milan this summer or at any stage in the near future.
"I've had a few offers but I want to stay here and lift trophies with this club," he told the club's official website.
"I'm the captain and I want to achieve great things with Inter.
"I've always shouldered my responsibility ever since I joined the club and I think the fans appreciate that.
"I've been given this opportunity as captain and I'd love to become a club legend like [Javier] Zanetti. Anyone would want to enjoy the same success he had."