The talks were preliminary and are not likely to be revived, the source said. UBS is not in talks with any other buyers for the unit but focusing on strengthening it, the source said.
In January, sources told Reuters that a Morgan Stanley broker who advised the investment bank's co-president James Gorman on his personal accounts quit to join UBS.
UBS declined to comment on the news, which was first reported by the Financial Times. Morgan Stanley could not immediately be reached for comment.
Last month Morgan Stanley agreed to combine its brokerage with Citigroup Inc's Smith Barney unit, paying Citi $2.7 billion and initially taking a 51 per cent stake.
Talks for a sale of the brokerage unit by the Swiss bank are not unexpected. Last summer, sources told Reuters that the bank was considering a sale of its US wealth management business, formerly known as PaineWebber, as part of a review of its business.
UBS bought PaineWebber some eight years ago for about $10 billion as a bridgehead into North America. UBS wealth management business in the United States has nearly 8,000 financial advisers and more than two million clients.
UBS, hobbled by $49 billion of losses on subprime mortgage securities and other assets during the past two years, received a $5.2 billion capital injection from the Swiss government on October 16. Switzerland took a nearly 10 per cent stake in UBS.
Last month UBS announced "radical" changes to its fixed income trading business, the primary source of the bank's losses thanks to an untimely expansion into subprime mortgages, collateralized debt obligations and other assets that became almost impossible to trade by the middle of 2007.
The bank has shaken up its capital markets management ranks, announced plans to slash its exposure to capital intensive businesses and cut thousands of jobs.