A deal between Lloyds and Lone Star has yet to be signed, the source said.
Lone Star’s bid is understood to have been backed by about £300m of senior debt from Royal Bank of Canada and Citigroup.
The Project Royal portfolio comprised about £1bn of debt secured against commercial property worth about £700m, the source said.
If the deal does go ahead, it will mark a further step in Lloyds’ ongoing efforts to reduce the £23.6bn of troubled loans held within its corporate real estate business support unit.
Lone Star and Lloyds declined to comment.
Earlier yesterday, real estate data provider CoStar reported that Lone Star had beaten rival bidders Cerberus and Colony Capital.
Royal Bank of Canada and Citigroup are arranging the finance for the Lloyds deal.
The sale of the Project Royal portfolio is the largest loan disposal by a UK bank since the collapse of the property market in 2008.
Lloyds, which has previously sold only individual loans, has this year sold the Mailbox building in Birmingham, raising £1.8bn.
It also completed a deal this month to sell 35 commercial property assets to property group Telereal Trillium. The sale is thought to have raised almost £45m for the bank.