West Ham visit Man United in a League Cup quarter-final on Wednesday before their next league game at home against Arsenal, who they held to a 3-3 draw last season thanks to an inspired hat-trick from Carroll.
"We are talking about a player who hasn't played since the game in Romania. For Andy Carroll, it should be good to play 20 minutes or half an hour for Saturday," Bilic told reporters.
"So, for Andy and every player in that condition it would be great to play a part, but if you are talking about 90 minutes on Wednesday and 90 minutes on Saturday, it is suicidal," he added.
"It should be crucial by the way, before you put him in from the start. You can't keep the players in the fridge and then throw them in and expect them to score again or score a hat-trick like he did at Upton Park.
"He wants to play every game, he's that kind of person. He likes to train, to play. It's about his knee... You have a scan, the opinion of the medical team and then we see how he feels."
West Ham will go into the League Cup tie without Senegalese striker Diafra Sakho, who injured his hamstring in the league draw with Man United at Old Trafford on Sunday.
(Reporting by Debanjan Bose in Bengaluru; Editing by John O'Brien)
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