The U.S. Treasury has told Bank of America (NYSE:BAC) it needs to increase its capital reserves by $39.9 billion within six months, bank officials said.

The shortfall, determined by the stress tests the Treasury Department conducted for the nation's 19 largest banks, may prompt Bank of America (NYSE:BAC) to convert the $45 billion it has already received from the government from preferred shares to common stock, which would increase the government's stake in the company, The New York Times reported Wednesday.

The stress tests, overall, are expected to show mixed results. Tests results for Bank of New York Mellon, Goldman Sachs and JPMorgan Chase are expected to show healthy reserves. These banks may even be allowed to return government funds issued through the Troubled Asset Relief Program, the newspaper said.

Citigroup (NYSE:C). is expected to need to further capital buildup. But Citigroup has begun negotiating to have government loans converted to common stock.

Bank of America (NYSE:BAC) 's Chief Administrative Officer J. Steele Alphin said there are "several ways," to raise capital, adding, "the company is very healthy."

However, "we're not happy about it because it's still a big number," he said. "We think it should be a bit less at the end of the day."