The City star limped off in the defeat to Liverpool with a hamstring injury earlier this month.
But Mancini has confirmed Tevez is responding well to treatment and is in line to lead City out at Wembley.
The main man: Tevez is set to return to first-team action in time for City's FA Cup showdown with Stoke
'We hope Tevez will be okay for the final' the City boss said. 'We have four weeks and he is doing well.'
City expect him to miss the next four league games as well, starting at Blackburn on Monday. Full-back Micah Richards is also ruled out of City's next game after missing the semi-final win over Manchester United with a hamstring problem.
Mancini added: 'Micah is not ready yet. He needs another week to ten days to recover.'
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