A number of accusations have been made against him, all from women who were models seeking work at the Daily and Sunday Sport newspapers.
Sullivan, who made his fortune from the pornography industry, denies the claims and says: "The false allegations levelled against me have been sensationalised by the media. After a lifetime spent building businesses in the adult industry in which I have met thousands of women, it is sadly inevitable that a small number of improper conduct claims are being made against me. I categorically deny these claims."
A spokesperson for the Independent Football Regulator said: "These are extremely serious allegations.
"We are in contact with West Ham on this matter and will use our statutory powers to seek urgent information from David Sullivan relating to his suitability under our Owners, Directors and Senior Executives regime.
"We are unable to comment further at this stage."
The 77-year-old had been on the board at West Ham for over 16 years before stepping down.
West Ham were relegated from the Premier League last month.
