The Belgium centre back, one of the key players in last season's title-winning campaign, has been sidelined since City's 1-0 victory over Stoke City in the fourth round of the FA Cup on Jan. 26.
"Vinny is getting better, we hope that he can recover for the next game, we will try for Monday for Aston Villa," Mancini told a news conference.
"But it is difficult because he didn't train with the team, he trained with the physio and we hope (he will return) for (next Saturday's meeting with Barnsley in the) FA Cup.
"The calf is a difficult injury."
Midfielder Gareth Barry is available after recovering from an ankle injury.
Champions City could trail leaders Manchester United by 15 points by the time they travel to Villa Park as Alex Ferguson's men host Norwich City on Saturday.
Mancini said 18th-placed Villa were a tricky prospect but that they simply had to overcome them otherwise last weekend's 2-0 victory over Chelsea would count for nothing.
"I think will be a difficult game because they play for relegation and will be strong and but for us, it will be important because if we don't beat Aston Villa, it is like we didn't do anything against Chelsea," the Italian said.
City have 56 points from 27 games, while United lead the way with 68 and third-placed Tottenham Hotspur are on 51.
Having overturned an eight-point deficit in the last six games of the season to win the title on goal difference last term, Mancini is concentrating on the maths.
"I was not strong in mathematics when I was at school but with 11 games to go, 33 points (are up for grabs)," he said.
"I think everything is possible ... The season is not finished. Our job is to play all the games 100 percent."