Avram Grant will give fitness tests to several players before deciding on his line-up for the game.
10 first-team regulars were not able to start or were suspended for the 3-1 win at Fulham, with Valon Behrami, Victor Obinna, Pablo Barrera, Mark Noble, Kieron Dyer and Benni McCarthy all playing no part at Craven Cottage.
Luis Boa Morte returns from a ban but Jack Collison, Manual Da Costa and Thomas Hitzlsperger are all definitely out.
Everton are hopeful Phil Jagielka will be fit for the game.
The England defender has had extra time to recover from the thigh strain suffered at Manchester City last week after the postponement of the Boxing Day game against Birmingham.
John Heitinga, who was also rated doubtful to face Alex McLeish's side, is hoping to overcome a knee injury. Midfielder Steven Pienaar (groin) is back in contention and Mikel Arteta returns from suspension but Victor Anichebe is banned. Leon Osman has been ill but is expected to feature.
West Ham (from): Green, Ben Haim, Tomkins, Upson, Gabbidon, Barrera, Stanislas, Kovac, Ilunga, Parker, Behrami, Dyer, McCarthy, Nouble, Spector, Boa Morte, Cole, Obinna, Piquionne, Sears, Reid, Faubert, Boffin.
Everton (from): Howard, Hibbert, Neville, Distin, Baines, Arteta, Cahill, Fellaini, Rodwell, Osman, Coleman, Bilyaletdinov, Pienaar, Saha, Yakubu, Beckford, Gueye, Baxter, Duffy, Jagielka, Heitinga, Mucha.