The Sun says Adebayor had a bust-up with Mancini at City's training ground last week over his recovery timescale after a leg injury and his lack of first-team opportunities.
Mancini said: "I don't know if he wants to stay or not. I think he must stay because he has a contract and he's an important player.
"It's a farce to say we fought in the dressing room or on the training pitch.
"We discussed the situation with his injury but on Monday he worked with the team."