Williams would move to New York from San Francisco

Last week, the New York Times reported that the search for the leader of the New York Fed was down to three people. Now, the WSJ reports that current San Francisco Fed President John Williams is the front-runner while "Raymond McGuire, the longtime head of corporate and investment banking at Citigroup and Mary Miller, a former top Treasury Department official, are the others.

The NY Fed is the most-powerful regional position because it regulates Wall Street and has a permanent vote at the FOMC.

The WSJ cities unnamed people familiar with the matter who say he has been recommended by the New York Fed's board for the top position after William Dudley steps down this summer.

Williams has been trying to move up at the Fed for some time. He was one of the final candidates for Fed vice chairman but that position will likely be given to Richard Clarida.

Overall, moving Williams to the New York Fed change the balance of the Fed and would simply move the search to fill a vacancy to the San Francisco Fed.