"I would really like him (Mancini) to continue here," said Tevez, whose relationship with the Italian manager was reportedly frosty last season.
"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 and it's the reason I have achieved such a high level.
"We are a team that is growing together. We are happy with what we've done so far but we know this season is our greatest challenge."
Mancini, who has been at City's helm since 2009, has no choice but to lead the Premiership side to success this season after the club's buying spree this summer.
Last term, the Citizens failed to secure a UEFA Champions League spot but they are widely expected to be in contention for the Premier League title this time around, thanks to their new arrivals.
City signed a good number of big names in the close season, including David Silva, Jerome Boateng, and Yaya Toure.
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