Officials from the Treasury and the Financial Services Authority are in talks with executives from Bradford & Bingley in a bid to secure its future.
A statement on its future will be made before the markets open on Monday, a Treasury spokesperson said.
B&B's share price has plummeted and it has announced plans to cut 370 jobs due to the downturn in the mortgage market.
A number of options, including the sale of B&B to another bank or nationalisation, are being considered.
"The Treasury, the FSA, and the Bank of England are working closely with Bradford & Bingley to consider the implications for their business of the recent financial turmoil," a Treasury spokesperson said.
Nationalisation followed by a swift sell-off of some of B&B's assets is a strong possibility, the BBC's political correspondent Iain Watson said.
The most likely bank to step in is Banco Santander, according to the BBC's business editor Robert Peston.
The Spanish firm which already owns Abbey and Alliance & Leicester has been looking at the British bank for some time.
Full nationalisation, which could well include merging B&B with Northern Rock, was very much the final resort if all else fails, Robert Peston said.
Liberal Democrat Treasury spokesman Vince Cable said it was imperative that whatever the solution for B&B, it must be decisive and there should not be a repeat of the delays following the crisis at Northern Rock.
Any takeover by another bank or banks of B&B will probably need some kind of financial support from taxpayers
"If the bank is in serious difficulty, the best option is if it were taken over by another bank and without any involvement by the taxpayer," he said.
"But the speculation in the national newspapers is that that won't happen and in which case it will effectively be nationalised, and that's what a takeover of Northern Rock actually means.
"I just hope this time the government doesn't faff around for four or five months getting this sorted out and just gets on with it."
All three of the main credit ratings agencies have downgraded B&B's creditworthiness, citing its problems raising funds and the excessive exposure of its mortgage book to buy-to-let and self-certified borrowers.
But Richard Pym, the recently-appointed chief executive, insisted the bank was "strongly capitalised" and was "fit for purpose going forward".
And Mr Cable said depositors should not panic because their money would be guaranteed by the government under the Financial Services Compensation Scheme.
The first £35,000 of savers' money in each banking group is protected under the scheme.
The prime minister was asked about B&B during his visit to New York for a UN development meeting.
He said: "I wouldn't comment, and nobody would expect me to comment, on these speculative statements that are made in newspapers.
"I'm not going to comment on any individual company or building society."
Conservative leader David Cameron also refused to comment on the situation at B&B.
But he said the Bank of England needed new powers to rescue failing banks.
Details of the plan, which is designed to stave off the threat to B&B and prevent a repeat of the Northern Rock crisis, will be outlined at the Conservative Party conference on Monday.
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