The retailer has announced plans to shut 31 of its 59 stores across the UK and Ireland as part of a rescue deal, impacting around 6,000 jobs.
It’s understood the retailer’s Edinburgh store in the West End of the capital has been identified for closure.
House of Fraser said it has already informed those whose jobs are impacted by its plans.
The closures are part of a proposed Company Voluntary Arrangement, which will require approval from creditors who will make their decision on June 22.
Frank Slevin, chairman of House of Fraser, said: “The retail industry is undergoing fundamental change and House of Fraser urgently needs to adapt to this fast-changing landscape in order to give it a future and allow it to thrive.
“Our legacy store estate has created an unsustainable cost base, which without restructuring, presents an existential threat to the business.
“So whilst closing stores is a very difficult decision, especially given the length of relationship House of Fraser has with all its locations, there should be no doubt that it is absolutely necessary if we are to continue to trade and be competitive.”
As part of the CVA process, House of Fraser also plans to relocate its Baker Street head office and Granite House office in Glasgow to new locations to help cut costs.
The company said it expects stores that are scheduled for closure to remain open until early 2019.
If the CVA is approved by landlords, it will affect up to 2,000 House of Fraser staff and a further 4,000 across brands and concessions.
It said the shops earmarked for closure would remain open until early 2019
The group said it also plans to relocate its Baker Street head office and the Granite House office in Glasgow to help slash costs and “secure House of Fraser’s future”.
Alex Williamson, chief executive of House of Fraser, said: “Today’s announcement is one of the most important in this company’s 169-year history.
“We, as a management team, have a responsibility to take necessary steps to ensure House of Fraser’s survival, which is why we are making these proposals.
“We are fully committed to supporting those personally affected by the proposals.”
House of Fraser said it has already informed staff set to be impacted by the plans, and was committed to “working with all those affected openly and with sensitivity over the months ahead”.
Hamleys owner C.banner is being lined up to buy a 51% stake in House of Fraser and invest £70 million into what remains of the business.
But its cash injection is pledged only on the condition the retailer can agree the CVA restructuring.
Will Wright, a restructuring partner at KPMG - which is handling the CVA, warned that House of Fraser would be at risk of administration if the CVA does no go ahead.
He said: “The business has been impacted by the mounting pressures facing the UK high street, with the declining profitability of certain stores exacerbated by costly legacy leases which were originally negotiated many years ago.
“With trading conditions unlikely to materially improve in the short term, the future of House of Fraser is at significant risk unless steps to restructure the business both financially and operationally are taken.”
A raft of CVAs have been struck in recent months as retailers struggle amid surging costs, rising business rates, competition from online rivals and a slowdown in consumer spending.