Virgin and Northern Rock's management team has been told by the Treasury to improve its offers to take control of the troubled bank, but insiders say their scope for doing so is limited.
The Government has indicated that bids must prove that the management team is a better option than nationalisation and has said it is not afraid of taking the bank into public ownership.
Virgin is the authorities' preferred private-sector option but it has been told to improve at least two features of its bid.
The Treasury wants Sir Richard Branson's consortium to increase the fee it is prepared to pay for the Government's guarantee of a £30bn bond sale.
The Government also wants a lower hurdle for it to take gains from warrants designed to give the taxpayer a stake in a recovery at Northern Rock.
The Chancellor, Alistair Darling, said yesterday: "We're in intensive discussions with Virgin but all options remain on the table. Remember I've got to take the right decision on the part, on behalf of the taxpayers who through the Bank of England are due to repaid a significant sum of money."
Virgin is likely to submit a revised bid by tomorrow as the pace of negotiations quickens. The Treasury is looking to make a decision in the second half of this month.
But Virgin is understood to have limited room to improve its offer, which would inject £750m into Northern Rock and raise £500m in a rights issue.
Olivant, Virgin's chief rival for Northern Rock, pulled out last week without submitting a formal bid, saying that the Government's terms were not commercially viable.
Northern Rock's in-house bidders, led by Paul Thompson, the former chief executive of Britannic and Resolution, was in discussions with the authorities yesterday to learn what changes were required. The in-house proposal would see shareholders inject £500m into the company, which would carry on as a going concern.
Mr Thompson's first duty is to shareholders and he will have to weigh whether an improved offer to the Government at the expense of shareholders would be used to extract more from Virgin, which most shareholders oppose.
Virgin said: "We remain in constructive discussions with the Treasury."