The Argentine forward's current deal with City runs out in the summer of 2014 and he is willing to continue playing for them.
"Yeah, I'd have no problem staying," Tevez told Sky Sports. "My family is here, my children are here, I'm happy, my wife is happy.
"I have two years on my contract, and, yeah, I could stay longer."
Tevez also said that last season's problems between him and manager Roberto Mancini are in the past.
"Last year was difficult for me," said the 28-year-old. "After I came back, I played and we were champions. That was the best bit of last season.
"The problems of last season are finished. Now I'm happy, Roberto [Mancini] is happy, the club is happy. The problem is finished."
Tevez was on target for City on Sunday as they drew 2-2 with Liverpool at Anfield in the Premier League.