First round bids for Iceland are thought to have fallen short of the £1.5bn asking price.
The frozen food chain, which has been put up for sale by its majority shareholder Landsbanki, has attracted bids of up to £1.3bn, according to the Mail on Sunday.
It is thought the banks organising the sale hope to achieve a deal by Christmas.
Morrisions and Asda are thought to have placed bids, but neither is thought to want to acquire the whole chain. Several private equity firms are believed to have places offers also Private equity groups TPG, Bain, Blackstone and BC Partners also submitted first-round bids,
Iceland founder Malcolm Walker, who runs the business currently, has not made a first round bid, but has the right to match any offer that is made to acquire the business. Iceland management, including walker, own 23% of the retailer.