Goalkeeper Fabianski is back in training after a hip problem and midfielder Snodgrass is battling to overcome a knee injury.
Liverpool forward Sadio Mane will miss the next two matches with a muscle tear but should return immediately after the club's mid-season break next month.
Manager Jurgen Klopp will restore his full-strength line-up having given most of them the day off for Sunday's FA Cup fourth-round draw at Shrewsbury.
He could bring back Fabinho for his first Premier League start since the end of November because of injury.
West Ham provisional squad: Fabianski, Zabaleta, Diop, Ogbonna, Cresswell, Noble, Rice, Lanzini, Fornals, Antonio, Haller, Randolph, Balbuena, Sanchez, Cardosa, Snodgrass, Ajeti, Ngakia, Kemp.
Liverpool provisional squad: Alisson, Alexander-Arnold, Van Dijk, Gomez, Robertson, Henderson, Wijnaldum, Oxlade-Chamberlain, Salah, Firmino, Mane, Adrian, Williams, Lovren, Matip, Keita, Fabinho, Jones, Minamino, Origi.