It says its commitment to mutual ownership "would benefit Northern Rock customers if it were to be remutualised as part of Coventry Building Society".
Such an outcome would see the stricken Northern Rock going full circle. Once a building society itself, owned by its customers, it demutualised and became a bank owned by shareholders. It came a cropper in the financial crisis, suffered the first run on a bank in a century and had to be nationalised.
The government relieved Northern Rock of its problem loans, keeping them in a hived off "bad bank". Now it hopes to sell what remains of the business.
Unions and some MPs have been campaigning for a return to mutual ownership. But UK Financial Investments, which is handling the sale on behalf of the government, has yet to set a timetable or decide how it will be done.