Sky News has learnt that Hilco Capital, which specialises in investments in distressed retailers, met Toys R Us UK executives earlier this week.
Hilco is expected to submit a letter of intent ahead of a deadline on Thursday for prospective bidders to express an interest in acquiring the struggling business, according to insiders.
A number of other, unidentified, suitors are also considering offers, they added.
Sky News revealed on Wednesday that Toys R Us was seeking bids for its loss-making UK arm before the end of this week as fears grow for the fate of more than 3,000 workers.
The truncated timetable underlines the precarious future of Toys R Us in Britain, just six weeks after it was thought to have been salvaged in an 11th-hour rescue deal.
The entire European operations of the ailing retailer are now on the market, encompassing 236 stores outside the UK in 10 countries including Austria, France, Germany and Spain.
The UK and European businesses are being sold through separate processes being run by Lazard and Alvarez & Marsal.
Sources said the UK faced the more imminent threat of bankruptcy, with a cash call at the end of the month meaning administration is inevitable without new funds being injected into the business.
That would leave a brand which has had a presence in the UK since 1985 potentially disappearing from the retail sector.
And one person close to Hilco said it was far from certain that it would lodge a formal bid.
The prospects of a solvent sale were unclear on Wednesday, with some potential buyers, possibly including Hilco, likely to wait until Toys R Us UK has crashed into administration before trying to pick off the most attractive stores.
Poor Christmas trading has left the British business facing cashflow issues, and one insider said it looked "close to unsaveable".
The company, which currently employs about 3,200 people in Britain, is already planning to shed up to 800 jobs through a process called a company voluntary arrangement (CVA), which was approved by creditors just three days before Christmas.
The CVA is intended to provide breathing space for Toys R Us UK to improve its fortunes by closing 26 of its loss-making stores and securing big rent reductions at many others.
Under that plan, which won the backing of 98% of creditors, including the Pension Protection Fund (PPF), its loss-making larger stores are due to begin closing in the spring.
The CVA deal secured the 11th-hour support of the PPF after the company agreed to pay almost £10m into its pension scheme over the next three years.
Without a new owner being found, the Toys R Us pension scheme, which is tens of millions of pounds in deficit, will be absorbed by the PPF.
Any such move is set to attract renewed attention from Frank Field, the Labour chairman of the Commons Work and Pensions Select Committee.
Shortfalls in defined benefit pension schemes are facing intense scrutiny following the collapse of Carillion, the construction group which fell into liquidation with a Section 75 pension deficit of £2.6bn.
Specialist toy retailers endured tough festive trading amid competition from Amazon and other online rivals, with Toys R Us now planning to close about 180 US shops - roughly 20% of the total - in the coming months.
In the UK, retailers including BHS, Focus DIY and JJB Sports have previously used CVAs to exit loss-making stores, although all three companies ultimately succumbed to the fast-changing retail environment.
New Look is now working on a similar plan, and House of Fraser is going through a process of seeking rent reductions from landlords.
The effort to overhaul its UK estate follows the filing by Toys R Us' American parent for chapter 11 bankruptcy protection in September.
There has since been controversy over payments to UK executives and the write-off of a big loan owed to the UK company.
When the CVA was approved, Steve Knights, the managing director of the UK business, hailed the "strong support for our business plan... so that we can better serve our customers today and long into the future".
A source said the full list of European countries where Toys R Us' operations were on the market also included Denmark, Finland, Iceland, Norway, Poland and Portugal.
In the US, Toys R Us won a court order this week to allow it to retain liquidators to close nearly 200 of its shops.
Toys R Us UK and Hilco declined to comment.