Tennessee, the program Kiffin abruptly left for USC early this year, declined the invitation.
Reached for comment on Wednesday afternoon, Tennessee athletic director Mike Hamilton said, "We told [USC] we could play 'em in a few years but we can't make it work with our schedule next year."
Hamilton said Wednesday he's been approached several times by Chick-fil-A Bowl president Gary Stokan about a potential 2011 matchup in Atlanta. Hamilton said it would be too much for the Vols' schedule, which already includes meetings with Cincinnati and North Carolina in addition to the regular Southeastern Conference schedule. Hamilton also said Kiffin had recently sent him some text messages about the proposal.
"We've got plenty to keep us busy in 2011 already," Hamilton said. "We're building our program back, and our schedule is tough enough as it is. The reality of it is if it was Texas or UCLA in the Chick-Fil-A Kickoff Game, we just couldn't do it in 2011."
Tennessee is scheduled to face North Carolina State in the 2012 Chick-fil-A Kickoff Game, and Stokan first asked Hamilton about his interest in playing in the 2011 game a few months ago against one of several possible teams. Stokan has approached Hamilton twice more since then, and Hamilton declined each time.
The Vols' tentative 2011 schedule as of now includes home games against Cincinnati, Georgia and LSU and road games at Florida, North Carolina, Alabama and Arkansas.
Hamilton indicated that the decision wasn't related to any hard feelings toward Kiffin, who left Tennessee abruptly in January after one season as head coach to take the USC job. The two schools have a verbal agreement to play each other in Los Angeles in 2021 and Knoxville in 2022.
"I know that sounds like a long time off, but we're awaiting a contract from them," he said.
The report of the Vols' decision not to play the Trojans follows an announcement earlier this week by sophomore defensive end Malik Jackson that he would transfer from Southern California to Tennessee for the 2010 season.
"Malik informed us of his intent to transfer to Tennessee in search of more playing time. We wish him the best of luck," Kiffin said in a statement.
Bruce Feldman is a senior writer at ESPN The Magazine. Information from The Associated Press was used in this report.