Tevez: FA Cup final fitness race for Manchester City striker
Tevez missed the semi-final victory against Manchester United last weekend after suffering a hamstring injury in the defeat by Liverpool.
City expect him to miss the next four league games as well, starting at Blackburn on Monday.
But Mancini believes the Argentina striker could be back to face Stoke at Wembley in the showdown on 14th May.
"I hope Carlos can recover in time as we have four weeks, " said Mancini.
Defender Micah Richards is also ruled out of the Blackburn game after missing the semi-final with a hamstring problem, but Mancini expects to have him available early next month.
Mancini added: "Micah is not ready yet. He needs another week to 10 days to recover."