Defender Kompany (groin) could miss the rest of the season while Bony (ankle/knee) faces at least another week on the sidelines.
Midfielder James Milner (knee), defender Gael Clichy (groin) and striker Stevan Jovetic are also ruled out this weekend.
West Ham will be without striker Diafra Sakho because of a thigh strain.
Forward Enner Valencia, though, is available after a minor foot problem picked up on his return from injury against Stoke last weekend. Defender James Tomkins (shoulder) and striker Andy Carroll (knee) remain sidelined.