The interview with a representative of the Auburn search committee took place in the past two days, AL.com reported, citing someone familiar with the process.
Strong denied the report, telling several reporters Wednesday that he has a job at Louisville.
Auburn's search committe is composed of athletic director Jay Jacobs and former players Bo Jackson, Pat Sullivan and Mac Crawford.
Former Arkansas coach Bobby Petrino is a candidate for the Auburn job, CBSSports.com reported Wednesday, citing a source.
Strong, 52, has a 23-15 record at Louisville, which announced Wednesday morning it was leaving the Big East and joining the ACC. The Cardinals are 9-2 this season and can win a share of the Big East title with a win at Rutgers on Thursday.
Auburn fired Gene Chizik on Sunday after a 3-9 season.