President Donald Trump is considering San Francisco Federal Reserve Bank President John Williams to be the central bank's next vice chair, a source told CNBC.

A separate source told CNBC that no decision had been made, adding that one is unlikely to be made next week with Trump traveling to the World Economic Forum in Davos, Switzerland.

Williams took over as the head of the San Francisco Fed in March 2011, succeeding current Fed Chair Janet Yellen. He started his career at the Fed in 1994. He is also a voting member of the central bank's policymaking committee this year.

This would be the latest change to the U.S. central bank by President Trump. Late last year, he nominated Fed Governor Jerome Powell to become the next Fed chair.

The Wall Street Journal first reported the interest in Williams for the vice chair job.