Sky News has learnt that Next and its fellow Reiss shareholder, Warburg Pincus, are working with bankers on an auction of the business, which was founded in 1971 by David Reiss.

Raymond James, the investment bank, is overseeing the sale process.

City sources said on Tuesday that the auction was in its second round, with a number of buyers circling.

Based on expected earnings before interest, tax, depreciation and amortisation in the current financial year of almost £65m, Reiss could be valued at in excess of £500m, according to the sources.

The identity of Reiss's suitors was unclear.

A person close to Next cast doubt on whether it would ultimately sell its 51% stake, while a senior retail executive suggested that it may be using the process to establish a market price and then acquire Warburg Pincus's remaining interest.

The process being run by Raymond James is understood to be soliciting offers for the entirety of Reiss's share capital, although Next could also opt to retain its 51% stake alongside a new equity investor, according to one source.

If it did decide to offload its shareholding, it would be a significant move for Next, which is run by chief executive Lord Wolfson.

Under his long stewardship, Next has delivered impressive returns for shareholders and transformed itself into Britain's clothing retailer.

In recent years, it has diversified by acquiring a string of distressed retail brands, often vying with the billionaire tycoon Mike Ashley to snap up ailing retailers.

It has struck joint ventures with companies including Victoria's Secret and Gap UK, while buying outright the baby products retailer JoJo Maman Bebe alongside hedge fund Davidson Kempner, and the fashion chain Joules.

The strength of its balance sheet has enabled it to wield significant muscle in negotiations with landlords during a period when traditional rivals such as Arcadia Group and Debenhams have crashed into insolvency.

It bought an initial 25% stake in Reiss in 2021, making a £33m equity investment to buy shares from Warburg Pincus.

Last summer, it exercised an option to take majority ownership of the chain by snapping up a further 26% shareholding.

Lord Wolfson described Reiss at the time of the original deal as "an outstanding brand with enormous potential".

Reiss's online operations have now migrated to Next's Total Platform, a technology service set up to handle smaller retailers' e-commerce logistics and sales.

The affordable luxury fashion chain trades from more than 60 UK shops, and has plans to expand its US estate of 7 stores threefold in the coming years.

As well as its own outlets, its men's and women's fashion products are also sold at Selfridges in the UK and Bloomingdale's in the US.

Next, Warburg Pincus and Raymond James all declined to comment.