Former St. Louis Federal Reserve Bank President James Bullard Tuesday said he spoke with U.S. Treasury Secretary Scott Bessent last week in connection with the White House search for a new Fed chair, and told Bessent that he'd be "happy to proceed however they want to proceed."

President Donald Trump is an outspoken critic of Fed Chair Jerome Powell, whose term runs through mid-May, and wants to pick a successor who agrees with his view that the central bank should be cutting rates.

Bessent is building a list of candidates that also includes National Economic Council director Kevin Hassett, former Fed Governor Kevin Warsh, a current Fed Governor Christopher Waller, and Marc Sumerlin, a former economic adviser to President George W. Bush.

Bullard signaled his own support for lower rates, telling CNBC in an interview that tariffs won't cause inflation but do appear to be slowing the economy this year, and predicting that the Fed would come around to that view and would cut rates by a full percentage point over the next year, starting in September.

He also said he would not be "dogmatic" about monetary policy, and noted that he was among those who pushed for sharply higher interest rates when inflation was rising sharply in 2022 and 2023.

"I'll accept the job if we set it up for success: if we can protect the value of the dollar...that'll give us lower interest rates over time; if we aim for low and stable inflation, (and) respect the independence of the institution under the Federal Reserve Act," Bullard told CNBC.

"We have to set this up for success, not for failure," Bullard continued. "If you want somebody to come into the job and fail, get somebody else; and I actually think anybody on this list would insist on that before they would take this job."