The Qatar sovereign wealth fund has emerged as the frontrunner to purchase Selfridges from the billionaire Weston family.
The Westons are said to have kicked off a formal sales process, placing a £4bn price tag on the department store chain.
The Qatar Investment Authority is in talks with the owners, but no buyer has yet been decided on. Selfridges declined to comment.
Other parties rumoured to be interested include Adia, the Saudi public investment fund, and Lane Crawford, the department stores business based in Hong Kong. Credit Suisse is said to have been appointed to oversee the sale.
A sale is likely to be not just for the UK stores, including those on Oxford Street in London and the Bullring in Birmingham, but also Brown Thomas and Arnotts in Dublin, De Bijenkorf in the Netherlands and Holt Renfrew in Canada.
The Qataris already own Harrods, after buying the Knightsbridge store from Mohamed Al Fayed in 2010 for £1.5bn.