The Belgium international defender picked up the injury during City's 3-0 win against Aris Salonika in the Europa League last-32 second leg tie at Eastlands. And, while boss Mancini is waiting to see how serious the problem is, it seems unlikely that Kompany will be fit to face the Cottagers this weekend.
"We won't know what has happened until tomorrow when we see what the situation is," said Mancini. "We have a lot of injuries at the moment, so I hope it is not serious and he will be available for Sunday."
Kolo Toure will deputise for Kompany if he fails to make the game, while Jerome Boateng is also capable of filling the void in the centre of defence.
Stuart Taylor will provide cover to first-choice keeper Joe Hart in the absence of shoulder injury victim Shay Given, while Micah Richards, James Milner are set to miss out with respective calf and hamstring problems. Nigel de Jong and Adam Johnson's ankle injuries will see them miss out too.