Paul Jewell, the Wigan manager, has described the offer as "not enough", with the club apparently determined to hold out for the £6m they are demanding for the French right-back.
Chimbonda has previously been courted by Tottenham, only for Wigan to turn down offers of £2.5m and £3m following his transfer request on the final day of last season.
Chimbonda, who joined Wigan last summer for £500,000 from Bastia, stunned Jewell and his team-mates by handing over a written transfer request within minutes of the final whistle sounding on the last game of the season at Arsenal.
With Chimbonda named in the Professional Footballers' Association team of the year and given a late call-up to France's World Cup squad, Jewell, and the Wigan chairman, Dave Whelan, made it clear they would not let the 27-year-old leave cheaply.
Spurs quickly found Wigan stubbornly refusing to budge from their £6m valuation, and now West Ham have also discovered Whelan to be as good as his word. Only last week, he said: "Chimbonda leaves this club for £6m only. He is a Wigan Athletic player for the next three years, unless somebody puts £6m on the table. As yet, that has not appeared.
"So I expect Chimbonda to swallow it and get on with it. If he doesn't knuckle down and get on with the job, he plays in the reserves; if he doesn't play well in the reserves, then he doesn't play at all.
"I'll keep him out of the game for three years if necessary," Whelan added. "It doesn't bother me what we have to pay him each week.
"So he has two choices; to pull on a blue-and-white shirt and knuckle down, or stay on the sidelines and kick a ball in the reserves. We sincerely hope he will buckle down and get stuck in again."
Wigan, meanwhile, have been warned they will not sign Denny Landzaat cheaply, either, as AZ Alkmaar are also demanding the going rate for the Netherlands international.
Landzaat has been linked with Wigan,although it is understood no official bid has been made, and Spanish side Espanyol are currently in the driving seat because they have made contact with the Dutch club.
With the midfielder likely to cost upwards of £5m, AZ spokesman Erik van Leeuwen said: "Denny is looking to pursue his career in another country, and we are willing to let him go.
"Denny is an international player with an ongoing contract [one year remaining] and we are not going to let him go for nothing. We don't want to block a transfer, but someone has to pay the right price."
Polish midfielder Tomasz Cywka has signed a three-year contract with Wigan. The 18-year-old agreed to join in March following a two-week trial, but was forced to return to Poland to complete his education.
Cywka has over 80 caps to his name for the under-18 and under-19 Poland sides, and recently became the second youngest player in Poland's history to be capped at under-21 level. After securing Cywka's signature, Jewell said: "I am delighted Tomasz is a Wigan player at last.
"He has a real chance to make it in the game. I think he has all the attributes to become a very good player as he has a great touch, vision and pace."
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