Recently hired Southern California athletic director Pat Haden told USA Today Reggie Bush was contrite in a 15-minute phone call last week.
But Haden told the Los Angeles Times Bush did not apologize for his actions, which played a role in the NCAA's sanctioning the school.
"Never did he say I'm sorry or I apologize," Haden told the L.A. Times. "Never did he say, 'I lied to the NCAA or I took stuff.'"
The NCAA found that Bush, now a running back for the New Orleans Saints, and his family received improper benefits during the 2004 and 2005 seasons. USC was placed on four years' probation, received a two-year bowl ban and had its scholarships reduced by 30 over the next three years. USC is appealing some of the penalties.
"He told me, 'If I could turn the clock back, I would. If I could give the Heisman Trophy back, I would,'" Haden told USA Today.
At the same time, Haden told the Times he did not consider that an apology.
"I would say it was conversation of him being contrite, but not an apology," Haden told the Times.
Bush spoke publicly last month about the NCAA's sanctions.
"Obviously, it does, but at the end of the day it is what it is," Bush said. "All I can really do now is focus on the New Orleans Saints and just try to move on. It bothers me and it sucks. The whole situation is terrible and nobody feels worse about it than I do.
"But, at the same time, I can't dwell on the negatives because I do have a job to do and I have a whole organization and a city riding on my back, not necessarily my back, but the team's back."
Haden said Bush was barred from visiting USC.
"I wish I could ask Reggie to come talk to our football team. I can't," said Haden, who replaced ousted AD Mike Garrett on Aug. 3. "He's not allowed on the campus. But I think he would tell them what a big mistake he made and how sorry he is."
Trojans coach Lane Kiffin downplayed the topic after practice Friday.
"I'm going to avoid that subject," Kiffin told reporters. "I think you guys already know my feelings for Reggie as a player and what he did here. I'm moving on.
"We've got too many good things going on here, with this team and what they're doing this upcoming season. Unfortunately, we end up talking about the past a lot. I'm moving forward."
Bush said he hopes his relationship with USC doesn't remain fractured forever.
"I hope someday at some point it can be repaired," Bush said when training camp started. "We'll see what happens. That's all I can do."
Information from ESPN.com's Pat Yasinkas and ESPNLosAngeles.com's Mark Saxon was used in this report.