The Hammers will be moving to the Olympic Stadium next season after more than a century at the Boleyn and still harbour hopes of finishing in the top four and qualifying for the Champions League.
"We are fully motivated and it is a massive game of course. It is massive for us and it is massive for them," he told reporters on Tuesday.
"It's the final FA Cup tie at the Boleyn Ground, it's Manchester United and it's the quarter-finals. It can't be bigger."
West Ham are sixth in the Premier League, five points behind fourth-placed Manchester City and one point behind United.
Bilic said, however, that the sole focus was on booking a trip to Wembley to face Everton on April 23 in the semi-final.
With the first tie ending 1-1 at Old Trafford, the Croatian sympathised with his Dutch counterpart Louis van Gaal, who has come under intense scrutiny this season.
"It's the stature of the club that they're not happy with losing games, with being fifth in the table. They are Manchester United and they have not been as consistent this season," Bilic said.
"But they are very capable of beating any team. It's hard to be a manager. It's the greatest job in the world, but at those massive clubs you're expected to win every game."
Bilic also heaped praise on striker Andy Carroll, who scored a hat-trick in Saturday's 3-3 league draw with London rivals Arsenal.
"Carroll, when he is fit and in form, is a very special kind of player. He is different...He doesn't have to score, but his presence on the pitch gives us another dimension," said the 47-year-old.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Alan Baldwin)
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