Private equity firms Apollo Management and Blackstone are understood to be in talks with the troubled bank - which is looking to reduce its balance sheet.
The loans form part of the funding that Citi provided for leveraged buyouts prior to the beginning of the financial crisis.
With the onset of the credit crunch, these loans have lost value significantly - and trade at around 90 cents to the dollar across the business.
Speaking to Bloomberg, William B Smith at Smith Asset Management was upbeat on the proposed sale.
"As a Citi investor you won't have to worry about more mark-to-market writedowns on these loans,'' he commented.
"There's now a consortium of private-equity firms saying what they're worth.''
Since the beginning of the year, shares in the bank have dropped 19 per cent - due in part to investors' concerns about the amount of 'bad debt' it is exposed to.
Citi declined to comment on the sale.