Dave Whelan has warned he will resign as chairman of Wigan if the Football Association punishes him for the controversy which has seen him labelled "a racist" by Cardiff owner Vincent Tan.
The FA has said its investigation into Whelan's comments about Jewish and Chinese people will be treated "as a priority".
It has written to the 77-year-old to seek his take on events.
Whelan spoke out in a newspaper interview where he was defending his decision to hire former Cardiff boss Malky Mackay and has since apologised.
Mackay was recruited by Wigan despite being under investigation by the FA for allegedly sending racist and anti-semitic texts, and Whelan responded to criticism by telling The Guardian: "I think Jewish people do chase money more than everybody else."
He also said he did not view the word "chink" - the term by which Mackay allegedly referred to Tan in a text message - as offensive.
Whelan told ITV News: "If the FA look into my affairs - and they were to find me guilty, which I hope they don't and I don't see anything like that happening because I'm absolutely anti-racist, always have been, always will be - however, if they have any questions I'm willing to answer it and, should they even suggest I'm guilty I would immediately resign from my position as chairman of Wigan Athletic."
Mackay has also denied being racist.
Malaysian businessman Tan, who sacked Mackay last December, told Sky Sports News on Friday: "Can you imagine if Mr Whelan was the head of the FA? Here we have a racist chairman hiring a racist manager. All the fans in Wigan now think it's okay to be racist.
"They follow the leader. So, how will the FA respond to this? I personally hope the FA is not a toothless regulator in this matter.
"What are Jewish and Chinese people thinking of the UK today? Action must be taken because the world is watching."
The FA said in its statement on Friday: "We are very concerned to read about the comments that have been attributed to Dave Whelan. We take all forms of discrimination seriously.
"As with all such cases, this will be dealt with as a priority. The investigation is already under way and the FA's governance division have written to Mr Whelan. He has three working days to respond."