Sports Direct, which last year bought department store chain House of Fraser out of administration for 90 million pounds, has a near 30 percent stake in Debenhams and has been trying to wrest control of it for months.
Ashley's latest move is an attempt to thwart Debenhams' restructuring and refinancing plan, which would give lenders more control over the retailer and could wipe out all shareholders.
The terms of the possible offer would be 5 pence a share in cash - a premium of 127 percent to Debenhams' closing share price on Tuesday of 2.2 pence, which valued the firm at 27 million pounds. Shares in Debenhams were up 50 percent at 3.25 pence at 0945 GMT.
Sports Direct said it would also assist Debenhams in addressing its immediate funding requirements but did not provide details. Debenhams' net debt at Jan. 5 was 286 million pounds.
Debenhams has not yet responded to Ashley's latest salvo.
Sports Direct's proposal is conditional upon Debenhams immediately appointing Ashley as its chief executive and terminating the noteholder consent solicitation process it announced last week.
That process is seeking agreement from bondholders to change the terms of some of their bonds so that Debenhams can secure new loans of up to 200 million pounds from existing lenders.
Debenhams has said that gaining those funds will allow it to pursue restructuring options to secure its future.
While Debenhams has warned that some of these options would result in no equity value for current shareholders, its preference remains a solvent re-financing of the business.
Bondholders have until Thursday to back the re-financing plan.
Sports Direct said on Monday it was mulling a possible offer for Debenhams but did not put a price on it. That move got a cool reception from Debenhams on Tuesday.
Under UK takeover rules Sports Direct has until April 22 to announce a firm intention to make an offer.
(Reporting by James Davey, editing by Louise Heavens and Alexandra Hudson)