Kompany has been on the sidelines for the past five games having suffered a calf injury during the 1-0 victory over Stoke in City's FA Cup fourth-round tie.
The Belgium international has been training with the club physio, however, having suffered a further set-back with his other calf, and Mancini feels the FA Cup quarter-final clash with Barnsley is a more realistic return date.
"Vinny is getting better in this moment," he said at a press conference. "We hope he can recover for the next game. We will 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.
He added, "The calf is a difficult injury because you think you are okay and then you have a problem. The calf is a strange injury."
Mancini is also positive on news regarding midfielder Gareth Barry, who has not featured in the squad since slotting past his own keeper in the 3-1 defeat at Southampton.
The former Villa player has missed his side's last two games with an ankle injury, but having returned to training this week, Mancini is confident he will be ready for Monday night's encounter.
"He has trained with the team the last two days and I think he will be ready," he said.