Smart, 37, has spurned several programs over the past few years, but sources told ESPN that he has significant interest in heading to Austin and replacing Rick Barnes -- who was fired this past week after 17 seasons.
"Nothing is done yet," one source close to the situation told ESPN.
However, discussions have occurred in the past 24 hours -- and one source said Smart is trying to get a feel for Texas athletic director Steve Patterson.
Smart has been the head coach at VCU for the past six seasons and became a hot commodity after taking the Rams to the Final Four in 2011. He has taken VCU to the NCAA tourney each of the past five years.
Barnes was named Tennessee's new coach on Tuesday.
Texas eyes VCU coach Smart to replace Barnes
College basketball Insider Jeff Goodman has the latest on VCU coach Shaka Smart's interest in the Texas head-coaching vacancy and how Smart could affect recruiting for the Longhorns.