Lloyds Banking Group is understood to have received an initial multi-billion-pound bid approach for Scottish Widows, its life assurance, pensions and savings business.
The approach has come from Edmund Truell, the founder of private equity firm Duke Street, who is currently bringing his £500m bid vehicle Tungsten to the stock market.
Analysts said that Scottish Widows could be worth between £5bn and £6bn.
Lloyds, which reports its first quarter figures today, is believed to have received a number of other approaches for Scottish Widows recently.
Antonio Horta-Osorio ruled out a sale of Scottish Widows this time last year after he conducted a review of all the bank's businesses when he became chief executive at the start of 2011, and the company yesterday said it had not received a formal approach, adding that the "insurance business remains a core part of the group".
But with increasing demands for banks and insurers to carry more capital by international regulators, a sale of Scottish Widows could once again be an attractive option.
Lloyds, which is 40 per cent owned by the taxpayer following the bailout of it and HBOS in 2008, is also having problems with its Project Verde sell-off of 630 branches, which the European Commission ordered because of the state aid it received. Last week it ended exclusive discussion with the Co-op and reopened talks with Lord Levene's NBNK bid vehicle.
Mr Truell has teamed up with his brother Danny Truell, chief investment officer of the Wellcome Trust, one of the UK's largest charities, to launch Tungsten.
It is understood that he has found "cornerstone" investors for the bid vehicle and that the full listing should happen in the middle of this month.
Tungsten would target "good sustainable financial services companies" across Northern Europe when he first launched the fund-raising.
He said: "We definitely want to buy businesses rather than assets. We will be targeting financial services businesses in the solvent part of Europe. "Never in my lifetime have there been more firms up for sale from the financial services sector and relatively little capital available to buy those businesses."
Mr Truell was unavailable for comment yesterday. Lloyds said it would not comment on speculation.
The bank bought Scottish Widows, set up in 1815 to support the widows and orphans of British soldiers killed in the Napoleonic wars, for around £7bn in 2000.