Mike Ashley's Frasers Group is reported to be in talks to save the high street giant.
It was announced last week that Debenhams - which occupies a large space in Brunswick Shopping Centre - would be wound down.
It is continuing to trade through its 124 UK stores and online to clear stock while seeking offers for all or parts of the business.
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After that, if no alternative offers have been received, all stores will shut.
The news came just hours after Topshop and Dorothy Perkins-owner Arcadia - which also has stores in Scarborough's Brunswick Centre - collapsed into administration, putting 13,000 jobs at risk.
Mike Ashley founded Sports Direct and also owns House of Fraser.
Frasers has reportedly said there is "no certainty" it can save Debenhams.