Lloyds TSB is in advanced merger talks with HBOS to create a UK retail banking giant worth £30bn, the BBC has learned.
A deal would end uncertainty about the strength of Halifax-Bank of Scotland after a run on its shares.
The government has also said it will over-rule any concerns that competition authorities may raise, BBC Business Editor Robert Peston has learned.
He added the prime minister was involved in negotiating the deal, which has the blessing of UK authorities.
HBOS and Lloyds have declined to comment.
The advanced talks are being encouraged by both the Treasury and Financial Services Authority (FSA) as a deal will ease concerns about the health of the UK banking sector, our business editor added.
The credit crunch has wreaked havoc on some of the world's financial institutions in recent days.
- Barclays Bank is to buy some Lehman Brothers assets after the fourth-largest US investment bank, filed for bankruptcy protection, dealing a blow to the fragile global financial system.
- The US Treasury stepped in with an $85bn rescue package to bail out AIG amid fears the group, once the world's largest insurer, could face collapse.
- Bank of America bought Merrill Lynch in a $50bn deal - making the Merrill the third top US investment banks to fall prey to the sub-prime crisis within six months.
- In Russia, trading on the country's main stock exchanges was halted after steep falls this week.
- Meanwhile, in the UK recent economic news has done little to lift the gloom, with unemployment rising once again as the number of job vacancies fell.
Our business editor said there was a real concern that any run on HBOS shares would create enough fear among the bank's financiers - providers of wholesale credit who give the bank its money - for there to be a withdrawal of credit for HBOS.
"Clearly the watchdog and Treasury will welcome a deal as it will put the bank on a sounder footing," he said.
"The last thing they want is a fully fledged crisis."
He added that the deal was negotiated at a very high level, with Prime Minister Gordon Brown telling Lloyds TSB chairman Sir Victor Blank that it would helpful if Lloyds could end the uncertainty surrounding HBOS by buying it.
"It was not in the government's interest for there to be the faintest risk that it would have another Northern Rock on its hands," he added.
Fears had been voiced that the proposed deal would face objections from competition watchdogs over the combined market share the enlarged group would have in mortgages and savings.
However, the government has since said it would over-ride the powers of the Office of Fair Trading and Competition Commission to push the deal through "in the interests of financial stability", our business editor said.
In an effort to avoid this potential stumbling block, the Treasury and the Bank of England have not been asked to help support the deal using taxpayers' money.
HBOS and Lloyds are instead relying on the Bank to push through a permanent successor to its current Special Liquidity Scheme, which lets lenders swap potentially risky mortgage debts for secure government bonds.
On the London market, HBOS shares have seen wild swings during morning trading, climbing as high as 220p and falling as low as 88p.
A buyout would create a banking giant that would be able to cope with the current crisis hitting financial markets across the globe.
While Lloyds would gain access to a larger share of the UK mortgage market, it would also be a case of "the bigger the better" as it would leave the enlarged bank on a sounder financial footing.
HBOS, which was created by the merger of the Halifax and Bank of Scotland in 2001, has come under pressure in recent days amid concerns about its exposure to the US sub-prime market.
Questions have been raised about whether it will be able to refinance its debt of more than £100m in coming months.
HBOS is the largest mortgage lender in the UK and has been hit by recent weakness in the property market. It also borrows a large proportion of its funding from the wholesale money markets where available funding has been drying up.
While the firm itself has offered reassurances about its financial health, the FSA has also moved to reassure the market saying the bank is "a well-capitalised bank that continues to fund its business in a satisfactory way".
"It is interesting to see this as an indication of the consolidation into the financial system," said finance expert Dr Paolo Subacchi, of think-tank Chatham House.
"We are clearly through a phase of restructuring and consolidation and the fact that two big players in the market are signalling their intention to merge is another sign that we are going in that direction."
James Ferguson from the stockbrokers Pali International added that the deal was a "second bite of the apple" for Lloyds as it had signalled its interest in taking over Northern Rock when the lender ran into trouble last year.
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