Sen. Richard Shelby of Alabama, the top Republican on the Senate Banking Committee, said Thursday that he will push for revisions to the Federal Reserve Act that would end the practice of bankers choosing the leadership of regional Fed banks.

"I believe this is an inherent conflict, because the banks decide who will be their regulator," Shelby said in an interview on CNBC. "I don't think that's a healthy thing."

The board of directors at each regional Fed bank is made up of three classes: Class A directors are elected by member banks to represent their interests, Class B directors are elected by member banks to represent the public and Class C directors are selected by the central bank in Washington to work on the public's behalf. Presidents are chosen by a group of directors, though the decision must be ratified by the central bank.

Though the Fed chairman and governors must win Senate approval, central bank officials have consistently rebuffed efforts to open the regional banks to a similar process.

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