The committee is working to name a finalist to replace retiring Justice Robert Rucker.
Brent Dickson is set to retire at the end of the month.
The finalists are Hamilton County Judge Steven Nation, Tippecanoe County Judge Loretta Rush and Indianapolis attorney Geoffrey Slaughter.
One legal analyst says there are two favorites for the job.
Former military lawyer and Boone County trial court judge to replace outgoing Justice Boehm