Ohio State this week identified Herman as the assistant with Smith at the club, a visit that was revealed in a school investigation into how Buckeyes head coach Urban Meyer handled domestic abuse allegations against Smith.
Ohio State has said Smith ran up a "significant bill" of nearly $600 of his own money at the Miami-area club in May 2014. Herman was the Buckeyes' offensive coordinator at the time. Ohio State could face an NCAA inquiry if the Buckeyes' assistants paid for high school coaches who were present.
"My wife knew exactly where I was, had no issue with it," Herman said. "I'm happy to cooperate, be honest, truthful, transparent with the NCAA if they so need me to be.
"I understand the responsibility that comes with being the head coach at the University of Texas. I take that responsibility very, very seriously. Right now, that responsibility includes me being laser-like-focused on preparing our team to win a game in less than 48 hours."
The No. 23 Longhorns open the season Saturday against Maryland in Washington.
Herman said he's had "some conversations" with school president Greg Fenves and athletic director Chris Del Conte. Herman would not address whether he or Smith paid for any high school coaches who were present at the strip club.
"Not until the NCAA asks me to," said Herman, who has been instructed by Texas not to address that specific question until the NCAA determines whether it wants to investigate the matter.
Herman left Ohio State to be the head coach at Houston in 2015.