There has been plenty of speculation over the Argentinian's future at City, with a number of top clubs from across Europe being linked with the player.
City have secured their place in the top four this season and moved into third place in the Premier League table with a 3-0 victory over Stoke City on Tuesday, thanks to a brace from Tevez.
If Mancini's men can beat Bolton on Sunday they will be guaranteed automatic qualification for the Champions League group stages next season.
The Italian manager is confident the club will have the services of Tevez going into the lucrative European competition next term.
He said: "I talk with him many times. I don't think we have a problem with him.
"He is a fantastic striker and a fantastic player for us and I think that he will stay here next year.
"He told me like this, that he wanted to stay. He has a five-year contract."
Punters can use their free bet to back City next season.