Sports Direct holds a 29.9% stake in Umbro, which Nike made an offer for last month. His holding would enable him to block the bid or force Nike to up its offer.
However The Financial Times reported that Ashley is "engaged in talks" with the US sportswear brand, signaling he may be willing to negotiate his position. However the newspaper said that Ashley had not given Nike any firm commitment backing its 195p a share offer.
Meanwhile the Office of Fair Trading is canvassing opinion across Europe from retailers and Nike's competitors about the bid. It may refer the deal to the Competition Commission for closer scrutiny if it deems it necessary.
Sports Direct rival JJB Sports also owns a 10% stake in Umbro but Nike has not yet held talks with the sports chain. JJB Sports acquired the stake to ensure it had "a seat at the table" in deciding Umbro's future. Both retailers are believed to be concerned that a Nike-Umbro company would give them worse terms.
Separately, Luminar chairman Alan Jackson is understood to have turned down the deputy chairman role at Sports Direct after he was linked to the position at the weekend.