Sky News understands that Arrow and Davidson Kempner, a hedge fund, are close to agreeing the purchase of a loan portfolio with a face value of tens of millions of pounds from UK Asset Resolution (UKAR).
Banking sources said that a transaction could be completed in the coming weeks.
A deal will be subject to approval from the Treasury, which oversees UKAR, the agency which holds assets previously owned by Bradford & Bingley and Northern Rock.
Ministers have been steadily reducing UKAR's balance sheet in recent years, and is also currently planning to sell a £5bn portfolio of taxpayer-owned mortgages.
The two current sale processes will allow the Treasury to close in on a publicly stated target of winding up UKAR by March 2020.
Investors including Pimco, the giant bond fund manager, have expressed an interest in buying the latest mortgage book being sold.
In the past year, UKAR has struck a series of deals, including the sale of an £860m portfolio of equity release mortgages to Rothesay Life, the specialist insurer.
Last April, UKAR struck a £5bn deal to sell a portion of its portfolio to an investor group led by Barclays and which included Pimco.
Cerberus, the hedge fund, has also been a purchaser of UK crisis-era loans, acquiring a £13bn portfolio of securitised mortgages in November 2015.
It is also said to be examining a bid for the latest tranche of mortgages.
The proceeds from the April sale were used to repay the outstanding £4.7bn of a Treasury loan to the Financial Services Compensation Scheme (FSCS), the interest on which is paid by major banks and building societies.
The return of the remaining sum marked another milestone in removing the legacies of one of the worst financial crises in British history.
Last autumn's tenth anniversary of the collapse of Lehman Brothers underlined the continuing repercussions of the 2008 crash, with interest rates in many western economies still at historic lows.
The Treasury sold a further chunk of shares in Royal Bank of Scotland last year, and aims to sell the rest of the government's stake within five years.
This week, it paved the way for further disposals through a mechanism called a directed buyback, which would allow RBS to acquire Treasury-held shares before cancelling them.
Meanwhile, the £20bn used to rescue Lloyds Banking Group has now been returned to taxpayers, generating a modest profit.
Tens of billions of pounds more has been yielded from the disposal of the customer base of Northern Rock to Virgin Money, and loans made by both it and B&B.
An Arrow Global spokesman declined to comment on Friday.