Set out in the 1978 Humphrey-Hawkins Full Employment Act, the Fed's current mandate is to set policy to influence inflation and employment.
The Washington Post reported Wednesday that Corker and Rep. Mike Pence, R-Ind., were backing legislation, which Pence would introduce, that would cut employment concerns out of the Fed's agenda.
In a statement, Corker said he had met with Fed Chairman Ben Bernanke in a private session. "At this meeting, Corker probed Chairman Bernanke on recent actions by the Fed. As a result of lengthy research and discussions, Corker believes now is the time to direct the mandate of the Fed to focus only on price stability," the senator's office said in a statement.
Some Republicans have been critical of the Fed's recent decision to buy $600 billion in long-term Treasury bonds, which would dilute the value of the dollar. There are fears the policy could promote unwanted inflation at a time of high unemployment.
The Post quoted House Financial Services Chairman Barney Frank, D-Mass., as saying the effort would amount to a "very dumb fight."
"The notion that the Fed should be indifferent to unemployment is a terrible idea, damaging to the economy," Frank said.