"Winston Reid is back from injury. He's one of our most important players. We will see if he is going to start," Bilic told reporters.
West Ham are without long-term injury victim Michail Antonio and fellow midfielder Sam Byram, who was sent off at Sunderland last Saturday.
And Bilic ruled out striker Andy Carroll, who returned to the starting lineup at Sunderland, after a recurrence of a thigh problem.
"He will probably be fit for our next game, but for this game, no," he said.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Everton have lost only twice in the league this calendar year and will arrive at the London Stadium with the league's leading scorer Romelu Lukaku, who has netted 24 goals in this campaign.
"It's a job for our defenders to stop him (Lukaku)," the 48-year-old Croatian boss added. "It's not only the defenders, though. We all need to stop the service to him.
"He is very consistent. He's been scoring goals all the time. Everton have done a great job to keep him and that shows how ambitious they are.
"He's not only one of the best players in the Premier League but in the whole of Europe."
Everton hold a significant head-to-head advantage against the London outfit having lost just once in their 17 previous league encounters.
(Reporting by Hardik Vyas in Bengaluru,; Editing by Neville Dalton)
