Debenhams shares were suspended from trading on Tuesday morning, pending a further update later in the day.
The new offer was dismissed by Debenhams as "highly conditional" and was rejected in part because Mr Ashley wanted to take over as chief executive.
Debenhams is now widely expected to fall into administration with the retailer's lenders seizing control. That is likely to mean store closures and job cuts while shareholders including Sports Direct will see the value of their stakes wiped out.
.The pre-pack administration undertaken by the struggling department store chain will see its debt reduced and comes ahead of a wider restructuring which will see around 50 stores close via a Company Voluntary Arrangement.
It will also see a £200 million refinancing plan, announced in March, go ahead.
Mr Ashley's attempts to take control of Debenhams had become increasingly desperate, and over the weekend the businessman demanded the board be investigated, two members to undergo lie detector tests and trading in its shares to be suspended.
Laith Khalaf, senior analyst at Hargreaves Lansdown said the struggle between Mr Ashley and Debenhams' lenders for control was now almost over, with the banks likely to emerge victorious.
"Clearly the Debenhams board has a number of stakeholders to consider and has to make balanced judgements about their interests, including those of its staff.
"But this latest swift rebuttal suggests that Debenhams simply isn’t interested in what Sports Direct has to offer.
"Mike Ashley’s tactics haven’t exactly been conducive to a convivial negotiation between Sports Direct and Debenhams, but nonetheless the business proposition should be judged on its own merits.
"It looks like Mike Ashley has one final card to play, and that’s making a firm takeover offer for Debenhams. Even that seems unlikely to shift the retailer from the course it’s currently on, as it sounds like the department store is preparing to enter administration imminently.
Additional reporting by agencies
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