Under the rule, the Federal Reserveis now incentivizing banks to keep less risky assets on their balance sheet. Because the deposits of small banks and hedge funds can be volatile, they require a lot of compliance and are expensive to maintain.
Last month, some hedge funds received a letter from JPMorgan stating that they would likely be charged for these deposits. Bank of America has also been targeting the deposits of hedge funds and smaller financial firms.
Read MoreJPMorgan continues run as top investment bank
The story was first reported by The Wall Street Journal on Sunday.
To Whalen, it's not only an issue of regulation but one of economics.
"The big banks can't make money on the huge inflows of deposits," he said. "The problem is the big banks can't deploy the funds.… They really don't want the money."
Read MoreHedge fund shutdowns heading toward 1,000
His advice: Go to a community bank.
"They want to lend the money. These big banks are so overregulated. They have operational issues, as well, that they just can't get out of their own way," Whalen said. "The smaller regionals, the community banks, want these deposits."
—CNBC's Kayla Tausche contributed to this report.