The Belgium international hurt a thigh during the 4-2 derby defeat at Manchester United last Sunday and a prognosis on the defender's recovery is not yet forthcoming.
"Kompany has a muscle injury - we don’t know how long he'll be out for. We don't know if he will be fit before the end of the season," explained the Chilean.
Pellegrini has a number of other injury concerns ahead of Sunday's Premier League clash with West Ham.
"Dedryck Boyata is fit. [Stevan] Jovetic, [Wilfried] Bony, [Gael] Clichy, [James] Milner and Kompany are not fit for Sunday.
"It's more important than ever to have the fans, the players and the staff together as one. We are one club."
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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
