The Chelsea reported a £39m loss in 2008
The Yorkshire and Chelsea building societies say they are in "advanced talks" about a possible merger.
The Yorkshire is the second largest building society in the UK, Chelsea is the fifth largest.
A deal would create a second large mutually owned mortgage and savings institution to rival the Nationwide.
In August, Chelsea reported that it had set aside £41m to cover to mortgage frauds, which helped push the society into a half-year loss of £26m.
The Yorkshire has two million members and 143 branches while Chelsea has 35 branches and 700,000 members.
"The board of Chelsea has been undertaking a detailed review of the society's activities, operations, financial position and corporate structure," the society said.
"As part of this, Chelsea has considered the potential benefits to members and other stakeholders of a merger and this has culminated in discussions with the Yorkshire.
Any merger is likely to be interpreted as a rescue deal for Chelsea, whose new chairman Stuart Bernau has been reviewing the future of the business and whether it can stay independent.
In 2008, it reported a loss of £39m, the largest recorded by a building society. It had to write off £44m, which was the bulk of its investments in two failed Icelandic banks.
Chelsea also wrote off a further £15m after buying a mortgage broker in 2007 whose business subsequently collapsed in the credit crunch.
Unlike banks and other stock-market quoted companies, building societies, which are owned by their members, have a limited ability to replenish their reserves if they are drained by losses.
"For a merger to proceed, the boards of both societies would need to be satisfied that it will be in the benefit of each society's members," they said.
"The merger would also be subject to approval by each society's members and the FSA."
It is not yet known if a merger would see a windfall for the members of either of the two societies. A spokeswoman for the Chelsea said no such details had been confirmed as yet.
Since the autumn of 2008 there has been a flurry of takeovers of small building societies to rescue them from problems brought on by the financial crisis.
In September last year, the Nationwide agreed to stage a rescue takeover of both the Cheshire and the Derbyshire.
The Yorkshire then took over the Barnsley building society, while the Skipton took over the Scarborough.
One of the UK's largest and strongest building societies, the Britannia, has merged with the Co-op bank.
In March this year, the Dunfermline building society collapsed, to be taken over by the Nationwide.
This was swiftly followed in June by emergency action by the authorities to ensure that the loss-making West Bromwich could stay afloat.