Reports in the Times today suggest that the supermarket giant has shown interest in buying the bank ahead of the general election.
Reports also suggest that the Virgin Group, which put forward plans to take control of Northern Rock in 2007, has expressed renewed interest.
A Northern Rock spokesman says: “We never comment on market speculation.”
Last week Moneymarketing.co.uk reported how Northern Rock will be split between two mortgage banks in the second half of the year.
The proposed restructuring will split the company into two separate entities. The first lender, “BankCo”, will hold deposits, branches and unencumbered mortgage assets. The second, “AssetCo”, will be made of the Granite master trust, all covered bonds, the Northern Rock mortgage book and all other wholesale instruments.