Payet told Bilic over the phone earlier this week that he would not play against Crystal Palace on Saturday in an attempt to force through a move from east London.
The 29-year-old, who cost West Ham £10.7 million from Marseille in 2015, was one of the stars of the Premier League last season and then shone at Euro 2016 for France.
That superb form earned Payet a bumper new £125,000-a-week contract, making him the highest-paid player in West Ham’s history.
But the midfielder’s performances have dipped this term amid continued speculation about his future, with Marseille and Paris St Germain believed to be weighing up bids.
However, Hammers manager Bilic has maintained his stance that Payet will not be sold this month.
Bilic dropped the bombshell during his pre-match press conference ahead of the Palace game. Tiring of being quizzed about West Ham’s pursuit of Brentford striker Scott Hogan, the Croatian dramatically changed the subject.
He said: “Let’s get serious. I have something to tell you. We have a situation with a player, Dimitri Payet. He wants to leave.
“The club, as I have said so many times, don’t want to sell him. We have said hundreds of times we don’t want to sell our best players. He’s definitely our best player.
“That’s why we gave him a long contract, and then a new contract a few months after he joined. I phoned him with that and he refused to play for us.
“He’s probably been tapped up by some clubs or whatever. That is usual at this time of year. But until he changes his attitude he is out of the team and he’s not going to train with us.
“But we are not going to sell him, not whatsover. I expect him to come back and show commitment and determination to the team, like the team has shown to him.
“Of course I feel angry. This team, the boys and the staff, gave him everything, they were always there for him. I am feeling let down and angry.
“It’s really frustrating and I have to look after my team, who are very committed and we can’t let this happen, no way, never.”
There were signs all was not well between Payet and the club when he was named on the bench for the recent FA Cup defeat by Manchester City, and then sent on by Bilic with West Ham 4-0 down.
This week’s development comes as yet another blow for Bilic in what has become a wretched first season at their new London Stadium.
The Hammers were dumped out of the Europa League by Romanian minnows Astra Giurgiu and have underperformed in the Premier League as both players and fans struggle to adapt to their new surroundings.
Nevertheless, Bilic is fighting on and pointedly vowed to replace Payet in the side to face Palace with a player with “character”.
He added: “We have to fill that hole. Let’s be honest, Dimitri Payet, when he is in top form it’s hard to replace his quality.
“But we will put a player in who has the character and the desire to help us replace him. Maybe we are going lose a player, but we are going to be a team.”