BHS entered administration in April. Since then, efforts have been continuing to rescue it from closure and save the jobs of its 11,000 staff.
Last week, a surprise late bid led by retail veteran Greg Tufnell transformed the race to acquire the retailer.
His team, said to be backed by Portuguese money, is the front-runner.
But if a deal cannot be struck, the business may still have to be liquidated.
The remaining bidders have faded into the background. Another consortium led by Matalan tycoon John Hargreaves and Turkish retail entrepreneur Cafer Mahiroglu has reportedly run into difficulties, while other suitors have apparently failed to impress with their proposals.
Some of those involved in the different bids have impressive retailing histories.
But then Sir Philip Green, who controlled BHS from 2000 to 2015, also had a brilliant track record. And he ended up selling the business for Â£1.
So what are the chances of saving BHS from the liquidators? And just who are the people aiming to do it?
In the public eye, Greg Tufnell is easily overshadowed by his more famous brother Phil, the former England cricketer.
But that could change if his bid for BHS is successful, because he hopes to become the firm's next chairman.
And as far as his credentials for the job are concerned, the 54-year-old executive certainly talks the talk.
He describes himself as "a highly experienced managing director with Mothercare and Arcadia, a blend of entrepreneur, strategist and hands-on operator with significant commercial business turnaround, acquisition and fund-raising experience".
His record shows that he was buying and merchandising director at Next from 1991 to 1994.
He then spent three years as managing director of menswear retailer Burton, part of the Arcadia group, followed by another three years as managing director of Mothercare.
He currently appears to occupy a portfolio of different jobs, including the chairmanships of leather accessories brand Zatchels and recruitment consultancy hga Group.
Earlier this month, he registered a new firm, Richess Group, at Companies House.
Its other directors are Nick de Scossa, a Swiss banker, and Lisbon-based entrepreneur Jose Maria Soares Bento.
Until Mr Tufnell's bid turned up, many observers had assumed that BHS would be snapped up by Matalan founder Mr Hargreaves.
But it appears that the cost of a deal may have proved too high. Sources say Mr Hargreaves was asked to improve his offer and balked.
Like Sir Philip Green, 71-year-old John Hargreaves also enjoys the life of the super-rich. He has an estimated fortune of Â£1bn, according to the Sunday Times Rich List.
But in stark contrast to the ebullient Sir Philip, Mr Hargreaves is described by industry insiders as quiet-spoken, someone who shuns the limelight.
Mr Hargreaves is no longer directly involved in the business he founded. He sold his 69% stake in Matalan in 2000, then in 2006 took it private through Missouri Bidco, a company 53.5% owned by him and his family.
As a partner in Mr Hargreaves' bid, there is also Cafer Mahiroglu, the owner of Select Fashions. At 50, he is the youngest of these High Street players.
Mr Mahiroglu's family owns a music store chain in Turkey and, crucially, factories across Turkey, Romania and Vietnam, which supply about 80% of Select's clothing merchandise.
Names that had been mentioned included Poundstretcher boss Aziz Tayub and Mike Ashley's Sports Direct, although Mr Ashley's proposal was reportedly rejected for being too low.
One factor that has complicated matters is that BHS has been selling off much of its stock in a discount sale, reducing the value of its assets and making it more expensive for any new owner to replenish the items.
If no deal can be struck, Duff & Phelps have already lined up three firms to act as liquidators. Alteri, Hilco and Gordon Brothers would then break up the business and sell it off piecemeal.
The 164-store chain includes about 40 loss-making shops. Freed from the need to take them all, many other bidders might be prepared to cherry-pick parts of the once-prosperous empire.
The fate of ailing department store BHS is likely to be decided later on Thursday, with an announcement expected from administrators Duff & Phelps.