LONDON—Royal Bank of Scotland Group PLC is close to naming Bank of America Corp. as a corporate broker, a move that would see the U.S. lender tasked with helping kick-start one of the largest privatizations in U.K. history, according to people familiar with the matter.

On Wednesday night U.K. Chancellor George Osborne announced that the U.K. government would start selling down its 79% stake in RBS. The British government's stake is currently worth just over £ 32 billion ($49.4 billion), well below the £ 45.5 billion that taxpayers injected into the lender at the height of the financial crisis.

Corporate brokering traditionally generates only nominal fees, but it is seen as a route for investment banks to gain more lucrative work advising on mergers and acquisitions and capital raises. These relationships can be among the stickiest and competition for them can be fierce.

Bank of America Merrill Lynch also acts as corporate broker to Lloyds Banking Group PLC, another lender which was bailed out by the U.K. government and is slowly being privatized. The U.S. bank earlier this year was named as joint broker to Royal Mail—the postal service in which the U.K. government sold a 15% stake worth £ 750 million via an accelerated book build Wednesday evening.

At Bank of America Merrill Lynch, Jim O'Neil, who leads the bank's financial institutions business globally, has worked with RBS in the past. Mr. O'Neil rejoined BAML in the autumn of 2013, after a three-year stint at U.K. Financial Investments, the body set up to manage the U.K. government stakes in, among others, RBS and Lloyds Banking Group.

The first shares sold by the government in RBS will almost certainly be at a loss. The stock is trading at £ 3.65, well below the average price of £ 5 a share paid in the bailout. On Wednesday Mr. Osborne said an initial sale would increase the bank's free float and pave the way for larger sales later. He said selling the entire stake could take years, while signaling a retail offer to the general public is likely to be part of the plan.

It is unclear when the RBS sell down will commence. The bank still needs to clean up a range of regulatory issues, including a large settlement with U.S. authorities over the sale of mortgage-backed securities. Industry watchers expect the bank to resolve the bulk of these issues by the end of the year.

RBS's current brokers are Morgan Stanley and UBS AG. UBS isn't expected to retender for the role because of conflict of interests with existing privatization work, according to a person familiar with the matter.

The British bank has been searching for new brokers ahead of the expected privatization.

Write to Max Colchester at max.colchester@wsj.com

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