FirstPlus, a sub-prime consumer loan business, will be sold at a knockdown price according to the newspaper.
General Electric Co and AIG are believed to be among the frontrunners hoping to acquire the business.
Frits Seegers, the head of Barclays' global retail business, had reportedly been running the auction of FirstPlus for several weeks.
The business is now expected to be sold for less than $9.1 billion, the value of its loan portfolio, and no premium is expected to be paid for the business itself.
It was valued at $9.9 billion in the summer but Mr Seegers had been ready to make a decision on whether to go forward with the sale last week but is delaying his verdict.
The news follows HSBC's decision to close its US sub-prime mortgage unit resulting in 750 job losses and taking $945 million in charges and write-downs.
Barclays sold most of its sub-prime credit card unit, Monument, to CompuCredit, the ES credit card issuer in April.