Lourdes Baez-Schrader sent out the brief statement Thursday.
It was the first indication that Williams was open to becoming a judge, which would require him to resign as the Republican leader of the state Senate.
The Burkesville Republican wields considerable influence as leader of the GOP-led Senate. He was trounced by Democratic incumbent Steve Beshear in last year's gubernatorial election.
Beshear, who has a record of appointing his Republican foes to higher-paying jobs, has said he believes Williams is qualified for the job of circuit judge.
A circuit court judgeship is open in Williams's district and Beshear must make an appointment to fill the two-year term.
