The other suitor is reported to be from private property investor London & Regional, run by Ian and Richard Livingstone. Their offer, valuing the supermarket at£1.04 billion, is believed to be in conjunction with Japanese bank Nomura.
Baugur, which had its potential offer of 190p a share rebuffed by the retailer in February is yet to revise its value for the retailer, but has not ruled itself out of the bidding.
Somerfield said it was in discussions with potential bidders last Thursday and that the board would meet to decide on the retailer's future in due course. A spokeswoman for the grocer refused to confirm whether the subsequent approaches had been made, but indicated that the board meeting was likely to take place within this week.