The “possible firm offer” would be for the 70 per cent of Debenhams shares that Ashley does not already own.
He would pay 5p per share, or £43m, in his latest attempt to seize control of the retailer.
Debenhams has so far resisted overtures by the billionaire, favouring its own £200m refinancing plan with its lenders which would wipe out existing shareholders such as 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, Ashley, who owns just under 30 per cent of Debenhams, would be immediately installed as chief executive of the high street firm.
Debenhams has said it will give any firm takeover offer from 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 £100m – 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.