USA Today Sports reported that Herman met with LSU officials in Houston on Thursday afternoon.
Florida State's Jimbo Fisher was also near the top of LSU's wish list, after being targeted last year when it appeared Les Miles might be fired. But LSU's search over the past few days shifted from Fisher to Herman.
Herman, in his second season as Houston's coach, was also thought to be a top candidate at Texas if the Longhorns fire Charlie Strong. Herman's Cougars play their final regular-season game Friday against Memphis, while LSU is playing its final regular-season game Thursday night against Texas A&M.
"I decline comment on that and any other report that's out there," LSU athletic director Joe Allevatold The Advocate minutes before the 25th-ranked Tigers kicked off against the No. 22 Aggies.
Texas president Gregory Fenves' preference has been to keep Strong, sources told ESPN's Mark Schlabach, and the odds of Strong returning for a fourth season are expected to increase dramatically if Herman is no longer available. The Longhorns need to beat TCU on Friday to finish 6-6 and become bowl-eligible.
Ed Orgeron has guided LSU for the bulk of this season after Miles was fired on Sept. 25 following an 18-13 loss to Auburn. The Tigers are 4-2 under Orgeron, who was a candidate for the full-time job.