The government would prefer to see the Rock sold to a bank rather than a private equity company.
It would mean that Lloyds would have to fight off the interest of JC Flowers, Cerberus and Sir Richard Branson who are all working on bids to takeover the bank.
Lloyds tried to buy Northern Rock in September though failed to reach an agreement with the government because it required considerable state guarantees but dissatisfaction with the Flowers and Virgin bids have been expressed by the government.
Any takeover from Lloyds would lead to heavy job cuts at the bank as staffing would overlap.
Northern Rock has already looked into the prospect of cutting jobs after it emerged this week that 2,000 employees could face the chop as a result of the slowdown in new business at the bank.