UK Asset Resolution (UKAR) is trying to sell £5.5bn of loans, with Pacific Investment Management Co (Pimco), Cerberus Capital Management, Och-Ziff, and M&G Prudential among the prospective buyers, Sky News reported.
The sale could take place as soon as next month.
Former Northern Rock and Bradford & Bingley mortgages are among the loans held by UKAR.
Around £11.8bn worth of loans were sold in March last year by UKAR to Prudential and Blackstone and managed by Computershare.
Many of these customers are now being transferred to Rosinca Mortgages and Jasper Mortgages, two brands created by Computershare.
And Cerberus bought a £13bn portfolio of mortgages from the government in November 2015.
Proceeds from sales are used to pay back Treasury loans.