The EU competition watchdog has been scrutinising Lloyds' business to ensure the bank, which was bailed out by the UK government last year, has not gained an unfair advantage over its competitors.
And now Brussels is nearing an agreement that would mean the group selling its substantial Lloyds TSB branch network in Scotland, while retaining about 300 HBOS branches.
It is also likely Lloyds will have to sell its Cheltenham & Gloucester branches, as well as internet bank Intelligent Finance.
The combined network of branches would make a "credible package" for a new entrant into the banking market, analysts said last night.
Read Bill Jamieson's analysis of this story here
Potential purchasers include Sir Richard Branson's Virgin Money, which has applied to the City watchdog for a banking licence, or Tesco Bank, which is creating 800 jobs in Glasgow at a new service centre. Spanish bank BBVA is also said to be interested.
Virgin Money said it was "working to make its bank ambition a reality" but would not comment specifically on whether it would bid for Lloyds' Scottish branch network.
The potential sale of Lloyds Banking Group's branches comes after the UK government gave the company 17 billion to keep it running at the height of the banking crisis last year. Prime Minister Gordon Brown and Chancellor Alistair Darling had waived competition rules to allow Lloyds to rescue HBOS.
Since then, however, EU competition commissioner Neelie Kroes has forced a number of European banks that received state aid to break up or sell off parts of their business.
Both Lloyds and the European Commission confirmed yesterday they were in "advanced discussions".
Ms Kroes said reports about the bank having to sell its Scottish branches was "premature speculation", while Lloyds declined to comment.
Jim Spowart – who founded the Bank of Scotland's online division, Intelligent Finance, and who campaigned against the takeover of HBOS by Lloyds – said a sale would be "a good thing for consumers and a good thing for employees as well".
But he added that the pressure on Lloyds to sell its assets was "needless".
"If they had kept the Bank of Scotland and Lloyds separate in the first place, they wouldn't have had to do this," Mr Spowart said. "It is a pity they didn't think about this at the time."
Martyn Evans, director of Consumer Focus Scotland, which campaigns for customers' rights, called for Lloyds to clarify the situation. "At the time of the banking crisis, consumers wanted stability and reassurance," he said.
"Now this has been achieved, there is the issue of effective competition in the retail banking sector.
"Consumers will want to know if any change in the ownership of Lloyds TSB branches in Scotland will help to deliver this."
Labour's shadow finance secretary Andy Kerr gave a conditional welcome to the potential for increased competition.
"There has been an expectation from those watching the market and the trade unions that steps would have to be taken along these lines," he said.
"In the first instance, I would hope that the workforce interest would be protected over the course of any change and, secondly, that whoever takes over these branches will provide good services to local communities, giving access to banking services as well as providing choice for consumers."
Lloyds TSB Scotland has 187 branches. The network was formed after Lloyds bought the Scottish Trustee Savings Bank in a 6bn deal in 1999. Together with its HBOS outlets, Lloyds has 500 Scottish branches in total.
The bank crisis – particularly after the takeover of HBOS – meant Scots had fewer banks to choose from. Up to 70 per cent of Scottish high street banks are now owned either by Lloyds or RBS, and Mr Darling has said he wants increased competition in the UK banking sector.
Analysts representing bank shareholders said the most important part of the Lloyds group was the 1,000 Halifax branches – and that it could sell its other branches or even its insurance arm, including Scottish Widows.
"As long as they keep Halifax. That is the most profitable part of the operation," said Jaap Meijer, of Evolution Securities.
The potential sell-off comes as Lloyds is due to announce plans to raise 20bn to try to boost its balance sheet and avoid the government's expensive insurance scheme for toxic assets. A rights issue would need to be approved by the Treasury and the EC.
Yesterday the bank confirmed reports that it was considering an appeal to investors to raise the funds, as well as selling off some of its assets to raise the money.
It also said it was "confident that the final terms of its restructuring plan, including any required divestments of assets, will not have a material impact on the group". After this assurance, its share price rose 7.5 per cent.
The bank hopes a sale of branches will raise funds that will allow it to avoid the government's asset protection scheme (GAPS), which, on terms agreed last spring at the height of the banking crisis, would cost Lloyds 15.6bn and insure 260bn of its toxic assets.
Experts said Lloyds' investors would be interested in putting more money into the bank if it could avoid the scheme. Paul Mumford, senior fund manager at Cavendish Asset Management, said: "Investors are likely to take a gamble on the long-term story for avoiding the GAPS, and would welcome the potential reversal to the dilution they currently face."