The group is called the Equity Trading Lab and a final decision has not yet been made, according to the Journal report.
Morgan Stanley was not immediately available for comment.
Wall Street banks are shedding their prop trading groups to comply with the Volcker rule, part of the recent Dodd-Frank legislation that prohibits banks from trading with their own capital for profit in securities and other financial instruments.
Goldman Sachs Group Inc
Morgan Stanley last month said it would spin off its Process Driven Trading prop trading group as an independent advisory by the end of 2012.
Its ETL prop trading group has generated about $100 million a year in revenue in recent years, according to the report. Daniel Ewig, Peter Bolland and Peter Fanelli help run the unit, which has fewer than 30 employees, according to the report.
(Reporting by Clare Baldwin; Editing by Dhara Ranasinghe)