The U.K. government said on Monday it would assist in the sale of troubled mortgage lender Northern Rock to private buyers by guaranteeing bonds issued by the firm.

Under a plan advised by Goldman Sachs, Northern Rock will raise funds from investors with bonds backed by the government's Treasury in case the assets of the lender are insufficient to fulfill the obligations.

Northern Rock would back the bonds with mortgages, securities and loans. The funds gained would be used to pay back the U.K.'s central bank, which provided over 25 million pounds ($49 billion) to Northern Rock to keep it from failing.

Potential buyers of the bank include Virgin Group Ltd and Olivant Advisers Ltd. In a statement, the government gave potential bidders until February 4 to submit a bid.

If no private proposal is suitable, the U.K. said it will take over the bank temporarily.

Shares of Northern Rock rose 29.75 pence, or 46 percent to 94.25 pence.