The FA's investigation into Whelan's comments about Jewish and Chinese people will be treated "as a priority".
Whelan, who has denied being racist, made the comments while defending his decision to appoint Malky Mackay.
"Should they even suggest I'm guilty I would immediately resign," he said.
In an interview with ITV News, Whelan added that he does not expect to be found guilty because "I'm absolutely anti-racist, always have been, always will be".
The FA issued a statement on Friday in which it said it was "very concerned" by the situation and had written to Whelan.
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The 77-year-old must respond to the FA by Wednesday.
Mackay was recruited by Wigan despite being under investigation by the FA for allegedly sending homophobic, sexist and racist text messages while at Cardiff.
Mackay, who took charge of Wigan for the first time against Middlesbrough on Saturday, has also denied being racist.
Whelan has apologised for remarks he made in an interview with the Guardian, although he has insisted he was misquoted and did not intend any racial slight.
The newspaper reported that Whelan used the word "chink" and also said that "Jewish people chase money more than everybody else".
"If I have upset one person, I apologise," said Whelan.
Tan, who sacked the 42-year-old Mackay last year in acrimonious circumstances, leading to a legal dispute, thinks the decision to make him Wigan manager is a mistake.
"This is a racist chairman hiring a racist manager," Tan told BBC Sport. "I hope that stops at two racists in Wigan, not snowballing to 2,000 or 20,000 racists in Wigan."
Both Whelan and Mackay have refused to respond to Tan's comments.
Dave Whelan says he will resign as Wigan chairman if the Football Association punishes him for the controversy in which Cardiff owner Vincent Tan has labelled him "racist".