Payet has netted six goals in 19 outings for the Hammers since his arrival from Marseille for £10m in the summer.
The 28-year-old has reportedly attracted interest in his services, but Bilic is in no mood to entertain offers.
"From my point of view there is no money in the world that we would let him go for," Bilic said ahead of his team's FA Cup fourth-round tie with Liverpool on Sunday.
"The things he does on the pitch, he also does in training. He is great to have in the squad and at the club.
"In previous seasons we were like a selling club, but we are moving stadium, we are talking and acting like we want to go up as a club, and for me the most important thing regarding that is not to sell your best players.
"Dimitri Payet, for me, no way. He is our player and he is staying.
"At this club there have been big players, but I think the last player who made such a big impact, in basically no time, is Paolo Di Canio."