The influential City captain has been out of action with a calf injury since the end of January and is unlikely to be ready for the Premier League trip to Aston Villa on Monday.
Mancini said: "Vinny is getting better in this moment. We hope we can recover him for the next game.
"We try for Aston Villa for Monday but it is difficult because he did not train with the team, he trained with the physio. We hope for the FA Cup on March 9.
"The calf is a difficult injury because you think you are OK and then you have a problem. The calf is a strange injury."
As for catching Premier League leaders Manchester United, who top the table by 12 points with 11 games remaining, the Italian added: "I think the season is mathematical.
"I was not strong in mathematics in school. Eleven games to play, 33 points, everything is possible. Last time we won the title: six games to go, eight points behind.
"Every game will be like this. When you are 12 points behind it is normal that if you don't lose or don't win and Man United win the next game it will be difficult."