Chris Cole, regulatory counsel for the Independent Community Bankers of America, told The Washington Post that many depositors see smaller institutions are seen as safer havens for their money.

"At times like this, people may feel it's time to shift to a bank that's nearby, where their neighbor may bank, where they may know the loan officer," Cole said.

It will be a few more weeks before the scope of the account transfers is known, the Post said Sunday. However, Cole told the newspaper most of the association's 7,000 member institutions are experiencing an upswing in community bank deposits.