Coventry Building Society said tonight that it believed Northern Rock customers would benefit if it were to take over the nationalised lender.
Britain's third biggest mutual was responding to reports that it was preparing a bid to acquire Northern Rock from the taxpayer.
The Government split Northern Rock in two last year, forming a mortgage and savings bank called Northern Rock plc and Northern Rock Asset Management (NRAM) to house the more toxic loans. It is the former half - the so-called good bank - which is preparing to return to private ownership.
Coventry Building Society stopped short of confirming its interest but said: "Coventry Building Society's commitment to mutuality has helped deliver consistently superior financial performance and member value throughout the financial crisis.
"The board believes that these credentials would benefit Northern Rock customers if it were to be remutualised as part of Coventry Building Society."
Northern Rock was nationalised in February 2008 after it collapsed amid the credit crisis, sparking the first run on a UK bank for 150 years.
Earlier this year, the Government launched a tender for advisers to look at options for Northern Rock plc, including a possible sale.
UK Financial Investments, which owns and manages the Government's bank stakes, recently announced the appointment of Deutsche Bank to advise it on options including a sale or flotation.
The bank earlier this week said it expects a further 680 job losses by the end of the year as it tries to return to profit and prepares for a return to private ownership.
Coventry Building Society said it "cannot rule anything out" but added: "The Government and UK Financial Investments have yet to confirm the process and timetable for the sale of Northern Rock. When that decision is made the board will examine the criteria laid down and decide the next steps to take.
"At this stage we cannot rule anything out but emphasise that whatever decision is made will be in the best interests of the society's members."
A successful bid would see Northern Rock remutualised by being absorbed into the Coventry Building Society's corporate structure.
Coventry Building Society, following its merger with Stroud & Swindon Building Society in September last year, has more than 1.5 million members and employs more than 1,600 staff.Reuse content