Mancini said last week that Tevez could leave Eastlands if he was unhappy at the Premier League Club after the pair fell out over the Italian's training methods.
On Friday, Mancini confirmed the duo had cleared the air and the striker, voted the club's Player of the Year this season, had no intension of seeking a transfer.
"I have spoken with him," Mancini told reporters.
"I asked him, 'are you happy to stay here?' and he said he was very happy.
"He says he wants to stay here, improve even more and help the club win things. He's a top player and one who is very important to this club."
Mancini, whose side missed out on securing a Champions League qualifying spot, will meet the club's owners next week to discuss his transfer budget as he wants make some significant signings during the close season.
"It's important that we buy players that can help us improve as a team next season. I don't know how many new players will be possible, but we will see," he said.
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