Possible buyers include HSBC and Standard Chartered, the newspaper said, citing industry sources.
HSBC said it would not comment on market speculation, while the other parties mentioned in the report could not be immediately reached for comment.
Two weeks ago Old Mutual propped up Nedcor with a $288 million loan and said the unit's losses would hurt group profits.
At the time, Old Mutual's Finance Director Julian Roberts said the move showed the company was committed to keeping the Nedcor stake. Old Mutual also appointed its strategy director, Bob Head, as Nedcor's acting chief financial officer.