The Weston family, which has a net worth of £11 billion in the latest Sunday Times Rich List, has lined up Credit Suisse to advise it on the future of the firm after receiving an unsolicited approach, React News reported.
The property news website added that it is understood bids in excess of £4 billion are likely to be sought for the overall business, with its real estate assets accounting for some £2 billion.
According to the report, the proposed sale would comprise the UK and Irish business, which includes the West End flagship store, and shops in Manchester and Dublin. Selfridges also has some sites it leases.
Department stores have been under pressure from online competition and changing shopper trends, while the pandemic hurt many chains in the form of closures during lockdowns.
Meanwhile footfall in central London is still suffering due to many tourists and office workers staying away.
But Selfridges has continued to offer additional ways to attract customers, from investing in online, to last month saying a newly acquired wedding licence will allow ceremonies to be hosted in its grade II listed building on Oxford Street for a limited time this year. Meanwhile, the rooftop restaurant there, Alto, has been transformed for the summer by Dior.
The founder of the store, Harry Gordon Selfridge, opened the London retail venue in 1909.