The company recently agreed to negotiate exclusively with the consortium consisting of private-equity investment firm Centerbridge Capital Partners LLC and Leucadia National Corp for the possible acquisition, the Journal said.
The potential value of the deal could not be learned, the paper said.
Citigroup is looking to sell the unit, which focuses on lower-income borrowers in North America, as part of a broader effort to shed assets and simplify the company's business under Chief Executive Vikram Pandit.
Citigroup declined to comment. Leucadia National and Centerbridge could not be immediately reached for comment.
(Reporting by Abhishek Takle in Bangalore; Editing by Gary Hill)