Consolidation in the wealth management industry has been a major theme since the 2008 financial crisis, as an increase in costs and regulation force some players to sell off units and others - like Baer - to seek to improve margins through scale.

"Given the early stage of these discussions, the outcome is entirely open," Baer said on Tuesday.

A spokesman declined to say whether Baer was interested in buying the whole business or parts of it. Sources told Reuters last month it was keen on units in Europe, the Middle East, Latin America and Asia excluding Japan.

A deal would be the biggest in the sector since Dutch group ING sold its private banking assets in 2010 to Julius Baer and Singaporean group Oversea-Chinese Banking Corp for a total of about $1.9 billion.

"For Julius Baer this would be a truly transitional deal, similar to the acquisition of the UBS private bank entities back in 2005," said Sarasin analyst Rainer Skierka.

The purchase of UBS-owned assets in 2005 marked the start of a major expansion and the end of majority control for the Baer family which established the bank in 1890.

If Baer were to buy the business outright, it would increase assets under management by about 50 percent from the 178 billion Swiss francs ($186 billion) the bank reported at end-April.

Skierka said a deal could boost Baer's Asian assets under management to 25 percent from 15 percent of the total now, in line with the bank's strategy to expand in the region where the number of millionaires is booming.

Vontobel analyst Teresa Nielsen said the deal could also increase the scale of Baer's European onshore business.

Like many Swiss banks, Julius Baer is keen to grow its presence onshore in Europe and offshore in Asia as the business of serving Western foreigners with secret accounts has come under pressure from a global clampdown on tax evasion.

Julius Baer has been on the prowl since it missed out in November on a majority stake in Swiss group Sarasin, which went to Brazilian-Swiss private bank Safra for $1.1 billion.

CNBC had reported on Monday that Julius Baer was close to a deal to buy the BofA unit.

"MASS AFFLUENT"

Reuters reported in April that BofA had put its wealth management unit outside the United States up for sale as the business, which manages $90 billion for rich clients, was not large enough to generate sufficient income.

Credit Suisse and Royal Bank of Canada were among those who put in initial bids to buy the business, sources told Reuters last month.

Nielsen and Skierka both estimated Baer had about 1 billion francs excess capital, so would probably have to issue new shares to fund at least part of the deal.

"Given its excess capital of 1 billion francs and expected cost synergies, financing of a reasonable purchase price via capital increase should become accretive," said Skierka.

Baer shares were up 1.7 percent at 33.08 francs at 6:27 a.m. EDT, beating a 0.6 percent firmer European banking sector.

"Questions still remain around the quality of the AUM for sale, its cost income ratio and profitability. We believe the acquisition could lead to high execution risk due to differences between Swiss and American cultures," Vontobel's Nielsen said.

The BoA business targets so-called "mass affluent" clients with hundreds of thousands of dollars, rather than super-rich private banking clients worth tens of millions, but it has failed to match the scale and profitability of its home market.

Bank of America has been selling off non-core business units 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.

($1 = 0.9547 Swiss franc)

(Reporting by Emma Thomasson; Editing by Dan Lalor)

By Emma Thomasson