While the former Manchester United striker has shown exceptional form this season, scoring 10 goals so far in the Barclays Premier League, he has at times looked ill at ease.
The Argentina international is struggling with homesickness, but Mancini said: "We can talk about this situation and talk about Carlos every week. I have explained it 1,000 times. Carlos is a fantastic player. He is one of the most important players in Europe and maybe in the world. He will stay here for a long time because he not told me otherwise."
Tevez will nevertheless sit out the match against his former club West Ham on Saturday as he is banned along with left-back Aleksander Kolarov, who was sent off against the Trotters.
Mancini is unperturbed by the duo's absence and remains confident his side can produce the goods at Upton Park and extend their unbeaten league run to seven games in the process.
He said: "Carlos and Kolarov are very important but the players who replace them can have a very good game.
"If we continue to play like we against Bolton and in the second half at Stoke (where City came away with a 1-1 draw) we can win without Carlos."
Defender Kolo Toure is expected to be available after returning to training following a calf injury that resulted in him coming off at the weekend.