The “possible firm offer” would be for the 70% of Debenhams shares that Mr Ashley does not already own.
He would pay 5p per share, or £43 million, in his latest attempt to seize control of the retailer.
Shares in Debenhams were up almost 50% at 3.3p on Wednesday afternoon.
It also emerged that Crispin Odey’s hedge fund, Odey Asset Management, has built up a stake of more than 5.2% in Debenhams, as well as a 7.9% short position.
Mr Odey, an influential financier, has previously backed Mr Ashley in a boardroom dispute. In 2017, he supported former Sports Direct chairman Keith Hellawell, who was kept on the board by Mr Ashley despite opposition from minority shareholders.
Odey Asset Management declined to comment.
Debenhams has so far resisted overtures by the billionaire, favouring its own £200 million refinancing plan with its lenders which would wipe out existing shareholders such as Mr Ashley.
In a statement late on Tuesday evening, Chris Wootton, deputy finance chief at Sports Direct, said: “Debenhams shareholders, both major and minority, are sick and tired of being ignored, cast aside and trampled underfoot by the lenders of Debenhams who, through the incompetence or, worse, collusion of the board, are allowing these critical stakeholders in the business to be wiped out. This is the shareholders’ chance to fight back.
“We reiterate our prior comments that we will leave no stone unturned in pursuing those responsible for this long-planned theft.”
As part of the condition of the Sports Direct proposed offer, Mr Ashley, who owns just under 30% of Debenhams, would be immediately installed as chief executive of the ailing high street firm.
Debenhams has said it will give any firm takeover offer from Mr Ashley’s Sports Direct “due consideration” but added that it would not solve its mounting funding crisis.
It said that, given the “timetable associated with any public offer”, a bid from Sports Direct would not address its immediate financing needs.
Sports Direct recently hit out at Debenhams for rejecting an offer to buy the chain’s Danish business, Magasin du Nord, for £100 million - one of several offers it has made to put the department store chain on a more secure footing.
The sports chain added that its proposals are better than the “multiple insolvency processes” Debenhams is considering as it looks to restructure.
In a separate development, Findel urged its shareholders to reject a £140 million takeover offer made by Sports Direct.
In a circular to investors, the board repeated its previous insistence the offer significantly undervalues the company, which is an online retailer and supplier of resources to schools.
Sports Direct made a mandatory offer of 161p per share in cash for the business earlier this month.
It has already increased its holding to 37%, taking it above the 30% threshold that triggers a mandatory bid under UK takeover rules.
Findel’s directors said the price offered was below its undisturbed share price before the offer was made public.