The securitisation firm's equity stake is thought to be worth as much as $8.5 million, with the sale set against very volatile conditions on the financial markets.
Morgan and Goldman Sachs have already said that they will switch from their current business-to-business models to becoming bank holding companies - giving them more protection from the Federal Reserve and allowing them to take consumer deposits for the first time.
These moves follow the collapse and subsequent takeover of Bear Stearns, the bankruptcy of Lehman Brothers and the $50 billion merger undergone by Merrill Lynch with Bank of America.
John Mack, Morgan Stanley's chief executive, commented: "Mitsubishi UFJ would be a valuable partner as we transition to a bank holding company and build our bank services and deposit base."
The Dow plunged again yesterday following Friday's rally, losing 3.27 per cent as investors showed a continued lack of confidence in the financial services sector.