West Ham United have rejected a second bid from Marseille of around £20m for Dimitri Payet with the co-chairman David Sullivan adamant the wantaway France international should apologise to supporters before he is allowed to leave the club.

Sullivan met the Marseille president, Jacques-Henri Eyraud, and the sporting director, Andoni Zubizarreta, in London on Monday to discuss their interest in the 29-year-old after he informed his manager, Slaven Bilic, that he wants to return to the south of France. Having seen their first offer of £19m rejected before the weekend, Marseille are aware of the delicate situation surrounding Payet and decided to offer only a small increase in their second offer, with West Ham holding out for a figure closer to £30m for a player whose contract expires in 2021 having only signed an extension last February.

Having initially stated that he would not be sold, Sullivan’s stance softened over the weekend and he appeared willing to allow Payet to leave for the right price. However, it is understood that West Ham will not be bullied into selling the player they purchased in July 2015 for £10.7m given they have no financial need to let him leave.

Payet will be fined for refusing to play in the 3-0 victory against Crystal Palace on Saturday and is expected to report for training on Tuesday, although he will be working with the under-23 side while the dispute is resolved. In an ideal world, Sullivan and the co-chairman David Gold would like him to make himself available for selection again and apologise to supporters for his actions but that appears unlikely with reports that his family has already returned to the south of France.

Captain Mark Noble admitted that he was “angry and disappointed” and hasn’t spoken to his team-mate for “two or three weeks”, while Gold appeared to refer to Payet on Twitter when he bemoaned the current situation.

“With a number of top Premier League players holding clubs to ransom is it time to close the January transfer window?” he wrote.

The current impasse could yet have ramifications for West Ham’s attempts to recruit further players this month. They have yet to return with an improved offer for Scott Hogan after Brentford rejected a third bid of an initial £9m which could eventually rise to £15m, with the Championship side unhappy with the structure of bonus payments. Crystal Palace and Watford are both monitoring the situation, with Brentford hoping to receive more up front given the fact that his former club, Rochdale, are due up to 30% due to a sell-on clause.

Any plans to allow Sofiane Feghouli, who scored the first goal against Palace and is wanted by Roma, to leave are also on hold until the Payet situation is resolved with West Ham keen to retain their squad for a busy run of fixtures.