The bank requested the meeting late last week, the people said.
The settlement is intended to resolve several investigations into the bank's packaging of risky mortgages into securities. One probe involves Merrill Lynch, which Bank of America agreed to acquire at the height of the 2008 financial crisis.
Mortgage securities helped fuel the housing boom in the mid-2000s and plummeted in value at the onset of the downturn, causing hundreds of billions of dollars in losses.
Sources said the Justice Department's silence about a meeting between Moynihan and Holder suggested Bank of America's request was premature.
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Bank of America has discussed paying about $12 billion, including more than $5 billion to help struggling homeowners, to resolve a range of federal and state probes, primarily into whether the company and its units defrauded mortgage bond investors in the run-up to the financial crisis, people familiar with the matter said.
The Justice Department suggested a $17 billion settlement in the latest round of negotiations and did not view Bank of America's offer as a serious one, one source said last week.
One sticking point is what the mix of fines and relief will be, sources said. Bank of America wants more consumer relief, they said.
Another issue is whether to include the bank's March settlement with the U.S. Federal Housing Finance Agency in the calculation, one person said.