Ashley is in advanced talks with Rangers chief executive Charles Green to buy a 10% stake in the club, according to The Herald.
If Ashley is successful, it will form a joint venture to sell the club's replica kit through his company, Sports Direct.
A club spokesman said: "It is speculation and we will not report on commercial matters."
However, a source said: "Talks are at an advanced stage and the deal should be signed in the next few days."
Rangers were recently demoted to the Scottish Third Division.