The Spain midfielder's current contract expires next summer, although the club have the option to keep hold of the 29-year-old until 2019.
Asked whether he would consider signing a new long-term deal with the Red Devils, Mata told ESPN FC: "Why not? I'm 29 and hopefully I can play football for some years.
"It would be great to play until I'm 40 like Ryan Giggs. But that's still a bit far - still 11 years.
"You never know what can happen in football and in life. But my feeling now is that I'm happy here and I wouldn't have any problem continuing here for more time."
Mata also revealed possible managerial ambitions.
"If you had asked me a few years ago whether I wanted to be a manager, I would say no," he said. "I think every footballer, after 20 years playing football, the first thing that comes to your mind is to relax.
"One, two years gap and do other things in life and enjoy other hobbies you might have. Right now, with years of understanding the game better, understand more the tactical approach or communicate with teammates, how to motivate them, I wouldn't say no to becoming a manager but I don't know."