Boateng, 22, signed from Hamburg last summer amid high expectations after he starred for Germany at the 2010 World Cup, but he has struggled with injuries.
Bayern director of football Christian Nerlinger said this week that the Bundesliga side were "keeping tabs" on Boateng, but Mancini insists the player is not for sale.
"I am happy Bayern have said this because it proves we signed a big player," Mancini said. "Jerome has had many problems this year, including three or four injuries, but he will be staying here.
"He is a big part of our future. If he doesn't have any problems next year, Jerome can be one of the best defenders in Europe."
City technical director Mike Rigg also dismissed suggestions Boateng could leave, although he did encourage Bayern to make a bid for Emmanuel Adebayor.
"Jerome is not for sale," Rigg said. "He will be very useful next season when we have Champions League games.
"Adebayor is a player who fit in in Bavaria - he's very similar to [ex-Bayern striker] Luca Toni."