Reports in France this week claimed Payet could be on his way to Manchester United, with fellow Frenchman Anthony Martial heading in the opposite direction.
Payet, who signed a Hammers contract until 2021 in February, has refused to be drawn on his future, but Bilic insists the France international will remain at the London Stadium.
“I can’t see any truth in that,” Bilic said. “Regarding Payet, not regarding Martial. He is a good player, a great player. But I don’t see this happening.
“Do I expect Payet to stay? Of course. Great players are always the centre of interest. Payet is one of the best in the world and they are always the ones who are linked with the big clubs. But I hope, and I expect, he will stay with us.”
While speculation about Payet’s future is likely to be a continuing theme of next month’s transfer window, West Ham have tied down another talent in the shape of Reece Oxford.
The highly-rated defender was a target for Arsenal, Manchester City and Manchester United but marked his 18th birthday by signing a new four-and-a-half-year contract at the London Stadium.
“It is great news for us,” Bilic said. “It is great news to sign one of the best talents, for him to stay with us for the long term, and it is a great thing for him as well. This is the best club for him to continue his development.
“The board have done a great job because it wasn’t easy to keep him. Those offers and interest from other clubs were not just rumours, they were real. We are delighted he is staying with us.
“Was he tempted by those offers? Probably, who wouldn’t be tempted when you are so young and you are bombarded with offers? But he has done the right thing.
“He knows that we like young players and he has already got his chance, and he knows that if he performs and proves himself in training and in games that he will get a chance here.
“He can be great. He has everything, composure, skill, steel in himself and technique. He has got great physical attributes. On paper, he is a great talent.”
Oxford will miss Saturday’s visit of Hull with an ankle injury as West Ham look for back-to-back wins to climb further away from trouble following the midweek victory over Burnley.
“That would be brilliant of course,” Bilic said. “We spoke about this couple of games in the period when we played against Spurs, Manchester United, Arsenal and Liverpool. It was an extremely difficult schedule. That period came and we started with three points and we have a really good chance [on Saturday]. Nothing can give you confidence better than victories.”
