Icelandic group Baugur is reported to be preparing a second bid for the Somerfield chain, in a bid to beat off two rival offers.
Media reports claimed the group is looking to move quickly, with a possible bid expected as early as next week.
Baugur, which already owns the Big Food Group, is thought likely to make an offer of between 210p and 220p a share.
In the meantime, Somerfield said it will be holding talks with two property consortia, which had approached it last week with offers.
Robert Tchenguiz, a property entrepreneur, backed by Apax Partners and Barclays Capital, has offered 205p a share, or £1.1 billion.
London and Regional, a private property company, has put forward a lower bid of 190p a share, but is thought to be considering a new offer in excess of 205p.
