The new suitor is understood to be one of the world's biggest financial institutions – but, crucially, does not have a major high-street presence in the UK.
The firm has made preliminary inquiries about HBOS, but is not as far through the process as the other alternative bidder, whose presence was disclosed in The Scotsman on Saturday.
The emergence of two potential new bidders for HBOS has thrown yet more doubt over the Lloyds TSB takeover, which has been received the backing of the UK government.
Alex Neil, a Nationalist MSP and member of the Holyrood finance committee, said he now believed the HBOS takeover by Lloyds TSB would not go ahead.
He said: "I am very optimistic, I am sure it will not go ahead.
"This (third] potential bid is from a financial institution outside the UK. Because the whole strategy here is not from somebody headquartered in London, they would not run into the same problems. This is a big, big, global player."
Jim Spowart, a leading Scottish businessman, has been in talks with Jim Murphy, the Scottish Secretary, for several days about another potential bidder for HBOS.
Mr Spowart said yesterday he did not know anything about Mr Neil's "third bidder", but he was clear the company that he is dealing with is "very, very serious" about HBOS.
The talks had reached such a detailed stage that Mr Spowart felt he had to bring in the UK government, which is why he began discussions with Mr Murphy.
Mr Murphy said the UK government would examine all potential bids on the same basis, despite the ministerial decision to waive normal competition rules last month to give the Lloyds TSB merger its blessing.
Yesterday, Gordon Brown said he would treat all bids equally, but stressed HBOS had been near collapse when the government and Lloyds TSB stepped in.
The Prime Minister said: "I think the important thing is that people are free to bid for HBOS, but we have got to recognise where it was – in a position where there was only one choice about rescuing it. Only one company had come forward at that time.
"We have invested 17 billion into buying shares in the new entity. I do think people have got to remember that if we had not acted a few weeks ago, HBOS would have fallen altogether."
He added: "Of course, we will look at every offer. That is part of the process of shareholders sorting out what the future is."
Experts expect all potential bidders to keep their identities secret until they have seen HBOS's trading position, which is expected this week.
If, as expected, HBOS reveals further multi-billion-pound writedowns, it could affect potential offers – the troubled bank is expected to unveil an additional hit of up to 5 billion when it updates the market.
HBOS warned last month that its profits were being squeezed by bad debts and asset value markdowns, while it was also suffering from increased funding costs in stricken wholesale money markets and falling property prices.
The expected heavy writedowns – due to come in a statement to coincide with a trading update from Lloyds TSB – will underline the trading troubles faced by HBOS as it seeks to secure the tie-up with Lloyds.
There will be further scrutiny on the Lloyds TSB proposals later this week, when the bank releases a circular to shareholders regarding its planned takeover of HBOS.
Lloyds has been reticent on the timetable of its announcement so far, saying only that it will be during the first week of November.
But, crucially, it is understood it will give an idea of its future financial footing, taking the HBOS acquisition into account.
Murphy under pressure over media leak
JIM Murphy, the Scottish Secretary, was facing calls for an investigation into his conduct last night following allegations he leaked confidential commercial information on HBOS to the media.
News of a second potential bidder for HBOS was published by sections of the media – including The Scotsman – on Saturday, with a comment from Mr Murphy insisting that all bids would be treated fairly.
But political opponents claimed Mr Murphy had been responsible for leaking the information, which could have compromised any rival bid to the Lloyds TSB deal, backed by the Westminster government.
Nicola Sturgeon, the Deputy First Minister, said if Mr Murphy had leaked sensitive information, there should be an inquiry. "If the Secretary of State did divulge confidential information about a possible alternative bid, that's a very serious matter indeed," she said. "I do think serious questions have to be asked and I think the matter does merit investigation."
David Mundell, the shadow Scottish secretary, said: "If there is any suggestion any politician has broken any confidences, that must be investigated."
And Liberal Democrat MSP Ross Finnie said: "I think questions ought to be asked."
Four futures facing banking giant
THE four options for HBOS are:
1 Takeover by Lloyds TSB. The most likely option, backed by the boards of both banks and the UK government.
2 Takeover or merger with first alternative bidder. It is not known who this potential bidder is, but it has been described as having a "very, very serious" interest.
3 Takeover by the new potential, third, bidder, understood to be a major international financial institution. However, talks are at a very early stage and the chances of this firm actually putting together a cogent bid are slim.
4 HBOS remaining as a stand-alone organisation, funded in part by the bank bail-out from the UK government. This is the favoured option for many politicians and business experts in Scotland.