Big Food Group has confirmed that Icelandic retailer Baugur has approached the company to discuss a possible £378m ($677m) takeover bid.
The Iceland chain has 760 stores across the UK and Ireland
Big Food, which also owns the Booker cash-and-carry business, said the offer could be worth 110 pence a share.
However, it stressed that there was no certainty an offer would be made.
Earlier, it declined to name the suitor, but speculation swiftly centred on Baugur, which already owns a 22% stake in Big Food.
Earlier this week, Baugur offloaded its 10% holding in House of Fraser to strengthen its war chest.
The group has built up a strong presence on the UK's High Street, where it already owns womenswear stores Coast, Whistles and Oasis. It also recently sealed a £120m takeover of fashion brand Karen Millen.
In May, Big Food posted a 35% jump in full year pre-tax profits before exceptional items to £50.1m ($91.2m).
But profits at the core Iceland chain have been deteriorating with like-for-like sales down 3.8% in the 10 weeks to September 10.
Meanwhile, sales at Booker fell by 4.1% during the same period.
Big Food said it expected tough competition to continue "for the foreseeable future".
Iceland has felt the pinch from market rivals Tesco and Asda, which have strengthened their market share by offering discount prices.
Retail sector analysts said the likely price mentioned by Big Food seemed generous given the company's problems.
"It's a pretty fair price as £250m of debt comes with this firm," said Richard Ratner, an analyst at Seymour Pierce.
"Iceland and Booker are businesses that are really struggling at the moment and the outlook seems to very constrained for them," said Clive Black, a broker at Shore Capital.
He pointed out that Big Food is saddled with high debts, a pensions deficit and a predominantly leasehold property portfolio.
"This current activity appears to be an initiative to try and do something to stem the tide of the erosion of the share price before things get really serious," he said.
On Friday, Big Food shares closed at 102.75p, up 11.4% or 10.5p.