Rodriguez met with South Carolina officials this past week to talk about becoming the replacement for Steve Spurrier. Rodriguez knows the state after serving as Clemson's offensive coordinator from 1999 to 2000, but turned down an offer to head back to South Carolina.
"Great news! @CoachRodAZ did not commit to the offer from S. Carolina. He's an Arizona Wildcat. #BearDown," Arizona athletic director Greg Byrne tweeted.
Rodriguez is 32-17 in four seasons at Arizona. The Wildcats will play in a bowl for the fourth straight season under him after finishing 6-6.
Happy and honored to be an Arizona Wildcat!! Bear Down!!— Rich Rodriguez (@CoachRodAZ) December 6, 2015
A source told ESPN's Joe Schad that Will Muschamp is still in the mix for the Gamecoks' head-coaching job. South Carolina officials have already had preliminary conversations with Muschamp, who's in his first season as Auburn's defensive coordinator. Muschamp, 44, was Florida's head coach for four seasons from 2011 to 2014, compiling a 28-21 record before being fired at the end of the 2014 season.
South Florida coach Willie Taggart interviewed Friday for South Carolina's opening. On Saturday, he received a five-year contract extension to remain coach of the Bulls.
Oklahoma offensive coordinator Lincoln Riley is also on South Carolina's interview list. Gamecocks interim coach Shawn Elliott interviewed Wednesday.
Information from The Associated Press was included in this report.