For West Ham, the competition represents a final opportunity to crown their farewell season at the Boleyn Ground, which stages its last ever FA Cup tie, with a piece of silverware.
Visiting manager Louis van Gaal, meanwhile, may need to win the FA Cup if he is to stand any chance of holding onto his job, after Sunday's 3-0 defeat at Tottenham Hotspur left his side four points off the Champions League places with only six games of the season remaining.
"And still we have one day less than West Ham United, because that's also important. But we have proved against Arsenal and Man City (in the Premier League) that in spite of less days to recover we could beat them.
"So I hope that we shall recover very good, also mentally, because this (losing to Tottenham) is again a blow of course. But everybody knows that this is the last chance.
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The venerable east London stadium, West Ham's home since 1904, will be charged with emotion and has already provided the scene for a last-gasp 2-1 victory over Liverpool in a fourth-round replay, as well as league wins over Tottenham, Liverpool and Chelsea.
minutes at Tottenham and Van Gaal could not disguise his discomfort at the thought of the bruising Carroll going up against Chris Smalling and the lightweight Daley Blind.
"I've seen the Andy Carroll Show," he said. "And (against Tottenham) I think our problem was also the miscommunication of our central defenders.
"I hope that we improve our communication because it is very important this game for us."
Carroll's time at West Ham has been hampered by injuries and despite the likely unavailability of fellow striker Diafra Sakho, Bilic refused to confirm if he would start on Wednesday.
"The medical team and the club are doing everything they can with Andy and he is doing it, but he should be even better if he can stay away from those injuries for a few years.
"Because it's a waste for West Ham, it's a waste for England, but it's the biggest waste for him.
"Will he start against Man United? I hope he's going to be fit for Man United. I don't think Sakho or (Alex) Song will be fit for that game."