The Sports Direct tycoon, who recently bought the department store chain out of administration for £90 million, has been in tense talks with landlords over rents in recent weeks.
Those negotiations have resulted in around seven House of Frasers being saved from closure, including in Oxford Street, Telford and Plymouth.
However, the tracksuit billionaire warned on Tuesday that “time is running out” for the remainder of the 59-store estate.
A spokesman for House of Fraser said: “Some landlords are being very collaborative in order to give us a chance at turning the business around, giving House of Fraser a lifeline and saving hundreds of jobs.
“However, some greedy landlords would rather see the stores close than help save the jobs of hundreds of people.
“We will continue to try and convince these landlords but ultimately time is running out. Some closures will be announced.”
It is understood that landlords are reluctant to agree to the low rents Mr Ashley is demanding.
Mr Ashley, who also owns Newcastle United, has pledged to save around 47 of House of Fraser’s 59 outlets since buying the chain.
He recently struck a deal to save House of Fraser’s flagship store in Oxford Street.
Mr Ashley said: “It is a massive step forward and further enhances our strategy of elevation across the group.
“My ambition is to transform House of Fraser into the Harrods of the high street.
“We will do our best to keep as many stores open as possible.”