The Belgium international, who has been sidelined with a calf injury since the end of January, is working towards a return to action against Barnsley in the FA Cup quarter-finals next weekend.
"Vinny is getting better in this moment," Sky Sports News quotes Mancini as saying. "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."
City remain 12 points adrift of Manchester United in the Premier League table.