The changes include a spinoff of the unit into a hedge fund or opening up the unit to outside investors, the people told the paper.
Morgan Stanley may still decide to leave the trading operation, called Process Driven Trading, as it is, the people told the paper.
Since its 1993 launch, the unit has earned the New York company $6.5 billion in pretax income, the paper said, citing a person familiar with the results.
A Morgan Stanley spokesman told the paper that no decisions have been made on PDT.
Reuters efforts to contact Morgan Stanley out of regular U.S. office hours were unsuccessful, while a spokeswoman from the company's office in Hong Kong was not immediately available to comment.
Morgan Stanley, on Wednesday, posted its third loss in six quarters and slashed its dividend as real estate investment losses and a debt-related charge wiped out strong trading and banking fees.
(Reporting by Ajay Kamalakaran in Bangalore; Editing by Muralikumar Anantharaman)