Skipper Tevez has had a transfer request rejected and, having been omitted from the dead rubber trip to Juventus, is due to meet the Blues manager at Carrington on Friday for talks.
Mancini said: "If Carlos is unhappy, and he's scored ten goals and played very well, then I hope that he's unhappy like that all season! But I don't think he is really unhappy. He can change his mind.
"Do I want him to stay? Absolutely. He has a contract, and he is our player. It's my belief that Carlos will stay with us, I think that he will continue to play for us.
"I will see him Friday morning. I will say 'good morning', and then we will talk. It's important that we speak, because we have a game with Everton on Monday and other very important games this month.
"I think that we can always change our minds. He's an important player here and it's an important season for us. We can change the history of this club.
Together, we can do good work here. I don't think he wants to leave
Patrick Vieira, who faces one of his former clubs in tomorrow's Europa League tie, insisted: "The players don't talk about it. He's been the same Carlos the last few days as he was at the start of the season."
Mancini has drafted several youngsters into the squad to face Juventus, knowing that a defeat to the Serie A side he supported as a boy cannot prevent City from qualifying for February's first knockout stage.
But the Blues boss said: "It's important that we finish first in the group. We don't want to meet a team from the Champions League in the next round, so it is important to the players that we win."