Just a handful of offers are thought to be on the table for Barclay Brothers-owned Shop Direct, which is on the market for around £3bn.
San Francisco-based private equity house Hellman and Friedman is now understood to be in the race, tabling a £2.5bn offer for the online retailer empire. The firm's other investments include Axel Springer, Germany's largest newspaper publisher.
The other reported bids are from former New Look investors Apax Partners, which is thought to have offered the full £3bn, and BC Partners.
City observers have raised concerns about the asking price for Shop Direct, which encompasses Littlewoods as well as Very.co.uk.
Shop Direct reported a 44 per cent jump in profits last year after becoming an online-only business. Fashion sales through Very have helped the company to post consistently strong growth during crucial Christmas periods.
But declining consumer confidence in the UK could threaten the company's sales, especially on big-ticket items such as furniture.
Some analysts also believe that consumer finance regulation will deter private equity firms from paying the full £3bn, as Shop Direct is among the biggest retail providers of credit in the UK to its customer base.
Other potential buyers which have decided not to put in an offer for the business are likely to re-enter the process if the asking price is lowered. However, sources told he Sunday Times that the Barclay brothers were prepared to abandon the sale process if there were no offers which met their expectations.
All parties have been contacted for comment. Apax and BC declined.