The London side could join the Merseyside outfit in the semi-finals if they get the better of Premier League rivals Manchester United at the Boleyn Ground in the quarter-final replay.
“Someone said to me this week that if we do get through to play Everton, we would definitely need to score two because Romelu Lukaku always scores against West Ham,” Bilic wrote in The London Evening Standard.
Lukaku is one of the best strikers in the Premier League and has been superb so far this season.
The Belgium international has scored 18 goals and provided six assists in the league for Everton this campaign.
The former Chelsea youngster has a great record against West Ham, having scored in six successive matches against the London outfit.
If West Ham qualify for the semi-finals of the FA Cup, then they will have keep Lukaku quiet in order to progress to the final.