Houston's Tom Herman, who has guided the Cougars to a 10-1 record in his first season as a head coach, is no longer a candidate for the South Carolina job, the sources said.
Smart, 39, has coordinated Alabama's defense during seven of his nine seasons on coach Nick Saban's staff. This season, No. 2 Alabama's defense is one of the best in FBS, ranking second in run defense (77.8 yards per game), third in scoring defense (14.5 points), third in total defense (268 yards) and sixth in pass-efficiency defense (99.8 rating).
Smart, who was named the 2012 American Football Coaches Association Assistant Coach of the Year and the 2009 Broyles Award winner, also worked on Saban's staff at LSU and with the Miami Dolphins.
Smart, a former Georgia defensive back, also would be considered one of the top candidates at his alma mater -- if the Bulldogs decide to part ways with longtime coach Mark Richt. Richt, who is in his 15th season at Georgia, is under increasing pressure after the Bulldogs were routed in earlier losses to Alabama (38-10) and Florida (27-3) and blew a 21-point lead in a 38-31 loss at Tennessee.
Herman, 40, directed Ohio State's offense in its national championship run last season. He previously worked as offensive coordinator at Rice and Iowa State and is considered one of the bright offensive minds in the sport.
Houston officials are trying to persuade Herman to remain at the school. The school has already approved a contract extension that would increase his annual salary from $1.3 million to $3 million, which he is currently considering. If Herman isn't a serious candidate at a top Power 5 job, sources said he might be inclined to stay with the Cougars.
The Gamecocks are seeking a replacement for former coach Steve Spurrier, who resigned after six games this season.