The 26-year-old recently criticised the Italian's training methods and has been linked with a move to Real Madrid.
But Tevez has come out in support of Mancini, whose future at Eastlands could be in doubt should he fail to take City into the Champions League.
"Of course I would really like him to continue here," Tevez told The Sun. "I would like all of us to stay and continue with this ambitious project which we have started.
"The manager has given me the continuity that every player needs to produce his best. He helped me recover my confidence.
"Thanks to the coach and my team-mates, things have worked well for me this season and it's the reason I have achieved such a high level."