Northern Rock is poised to name a consortium led by Sir Richard Branson's Virgin Group as favourite to buy the bank, the BBC has learned.
Northern Rock bidders were quizzed over the weekend
The bank is expected to name the group as its preferred bidder on Monday.
Virgin's bid includes an immediate repayment of £11bn of the £25bn the bank owes the Bank of England, with the rest to be repaid within three years.
If the bank's shareholders block the deal - which has Treasury approval - it could be taken into administration.
BBC business editor Robert Peston said: "Right to the last, the Treasury has been considering a radical alternative, which was to nationalise the bank.
"But it appears to have decided that taxpayers' interests are more likely to be protected by a private-sector solution."
Of the 10 expressions of interest from financial institutions in taking control of Northern Rock, Virgin's was preferable because it offered the best deal to the stricken lender's shareholders, Mr Peston said.
"Under the Virgin scheme, the Rock's shareholders would retain around a third of the Rock and would also receive a share of any future gains made by the new owners," he said.
If investors, which include hedge funds RAB Capital and SRM Global, are unhappy with the terms offered and resist the deal, he warns that the company and the government could say that the only alternative left is to put the bank into administration under insolvency procedures.
"If the Rock went into administration, shareholders might end up with nothing," Mr Peston added.
Solution in sight?
The Treasury has been under mounting pressure to agree on a solution for Northern Rock following criticism over the length of the sales process.
The Conservatives and Liberal Democrats have voiced concern over the likelihood of the hefty taxpayer-backed Bank of England loan, which has been propping up Northern Rock since September, ever being repaid.
In a letter to Bank of England Governor Mervyn King, Lib Dem acting leader Vince Cable had said that further delays in resolving the bank's future were "unacceptable".
He argued the best way to safeguard the billions of public money on loan to Northern Rock was for the government to temporarily take control of the stricken bank and then sell it in due course.
"Taxpayers cannot be expected to continue to prop up this sinking ship, especially as much of our money is likely to get lost at sea," he added.
Over a fraught weekend, officials from the Treasury, the Financial Services Authority and the Bank of England grilled a number of suitors on their plans to save the troubled lender.
In the end, it came down to a two-horse race, between the Virgin team and a proposal made by US buyout firm JC Flowers, Mr Peston said.
Under the terms of the Virgin bid, the Bank of England will keep an emergency credit line in place to be paid off on the same terms as a commercial loan arranged by Citigroup and Royal Bank of Scotland, according to Mr Peston.
This has been arranged by the consortium, which includes insurance firm AIG, to refinance part of the Bank of England loan and avoid it being viewed as illegal state aid.
If a deal is successful, the government will continue to guarantee Northern Rock's savings deposits, both new and existing, for three months after which time it will withdraw the facility.
Virgin has agreed it will only pay itself "normal" dividends from Northern Rock until all public money is repaid - thus avoiding the potential embarrassment for the Treasury of the group making spectacular profits with the help of the taxpayer-backed loan.
The new company would be rebranded Virgin Money, though it would keep its existing stock market listing.
Former boss of Lloyds TSB, Sir Brian Pitman, would be the bank's chairman.
But Virgin's plans could still be thrown into disarray by the bank's largest shareholders.
Hedge funds RAB Capital and SRM Global, which together own about 13% of Northern Rock's shares, have warned that they would not support a fire sale of all or part of the bank's assets.
They have indicated that they preferred to wait for the crisis-hit credit markets to settle down before considering a sale.
RAB Capital's chief executive Philip Richards told the BBC on Saturday that he would vote against a proposed takeover of Northern Rock that would "wipe shareholders out or nearly wipe shareholders out".