The Belgium international and City captain limped out of City's FA Cup fourth-round victory over Stoke City, and he missed the club's 0-0 draw with QPR on Tuesday.
Mancini has now indicated that Kompany will be sidelined until after the fifth-round FA Cup clash with Leeds on Feb. 17, which means he will also sit out the home clash with the Reds as well as the trip to Southampton.
"Vinnie is out," Mancini told reporters. "I hope he can recover after the FA Cup."
If the initial assessments are correct, Kompany's first game back is likely to be City's home game against Chelsea on Feb. 24.
Midfielder Javi Garcia was forced to fill in at the back against Harry Redknapp's QPR side, with Kolo Toure at the Africa Cup of Nations and Matija Nastasic not fully fit, though the latter is likely to return to first-team action against Liverpool.
Micah Richards, who has been missing since being stretchered off against Swansea back in October, is also due back in early February.