Tevez was forced to sit out 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 his Argentinian skipper could be back to face Stoke at Wembley in the showdown next month.
"I hope Carlos can recover in time as we have four weeks, " the City boss said.
Full-back Micah Richards is also ruled out of the Blackburn game after missing the semi-final with a hamstring problem.
Mancini added: "Micah is not ready yet. He needs another week to ten days to recover."
Source: PA
Source: PA