The former Inter Milan star has been involved in a number of incidents on and off the pitch, the latest being a red card offence as well as a dangerous tackle on Alex Song during City's 1-0 defeat to Arsenal on Sunday.
Reports have suggested that the 21-year-old could be on his way out of the Etihad Stadium in the summer but Mancini has vowed to stand by the frontman.
"If he wants to stay, he can stay - but he needs to change in his mind," Mancini said. "I don't change him. I spoke with Mario a lot of times about this. Ten years here with me might be impossible, but he can stay here two years, three years, more if he changes his behaviour. It is important."