Terms of the deal are still being finalized, but Julius Baer could pay $1.5 billion to $2 billion, CNBC reported.

Reuters reported in April that Bank of America had put its wealth management business outside the United States up for sale. [ID: nL6E8FHACU] The business, which manages some $90 billion for rich clients, is not large enough to generate enough money for the U.S. bank, sources told Reuters.

Bank of America and Julius Baer declined to comment on the CNBC report.

Bank of America has been selling off non-core business units under Chief Executive Brian Moynihan to build capital. The second-largest U.S. bank by assets has trailed rivals in recovering from the financial crisis, largely because of huge losses and lawsuits tied to its 2008 acquisition of subprime mortgage lender Countrywide Financial.

Bank of America's non-U.S. private banking business targets so-called "mass affluent" clients whose wealth is measured in hundreds of thousands of dollars, rather than super-rich private banking clients worth tens of millions.

But outside the U.S. it has never been able to build up the business to match the scale of its home market, meaning it is far less profitable.