The Belgian centre-back has been troubled by a thigh injury he picked up in the first half of last month's 3-1 win over Everton.
It now looks like he will sit out games against Norwich City, CSKA Moscow and Sunderland, although the Chilean coach is confident that the team can cope without the 27-year-old.
"Vincent is progressing but I think it will be after the international break maybe that he will be fit," Pellegrini told reporters. "Before that I think is difficult.
"He is a very important player but I think we have a strong squad just for this case. We played the last five matches, won four and lost just one against Chelsea, and I think we deserved more.
"So he is always an important player, but I think we can play also without him."
Pellegrini hopes that Kompany will be fit for City's home match against Tottenham Hotspur on November 24.