In 2004, Southern California claimed the national championship after a 55-19 rout of Oklahoma in the BCS title game.
Auburn also completed an undefeated season after beating Virginia Tech in the Sugar Bowl but finished second in the polls.
USC was subsequently stripped of that title because of numerous NCAA violations. Now Auburn is looking into whether it should recognize more than the two national titles they are traditionally given credit for.
The program won national championships in 1957 and 2010.
Former coach Tommy Tuberville, now at Cincinnati, said he got "no help" from Auburn officials trying to recognize the team as national championship after the NCAA came down hard on USC.
"They didn't step up and say anything," Tuberville said, via USA Today.
That I was disappointed with is we didn't have the media step up and say, 'OK, there's got to be a champion so who is it? It obviously should have been us," Tuberville said. "Oklahoma lost. Maybe they could say it should be split because they played in the game. But Auburn went undefeated.
"If it'd been Michigan, if it had been Alabama, there would have been more of a push toward saying, hey they should be named No. 1. But Auburn, for some reason, we never got to first base on it. There was no support out of the administration."
The program is also claiming titles in 1913, 1983 and 1993. The 1983 team finished 11-1 and 1993 team went 11-0 but was on probation and banned from postseason play.STAPLES: SEC officials adjusting to hurry-up offense one jog at a time