"I have the best job in the country," Strong said.
Hurricanes coach Al Golden was fired on Sunday, and sources told ESPN's Brett McMurphy on Monday that Strong is a candidate to replace him.
Strong was asked again at the end of his weekly news conference to clarify whether he was interested in the Miami job.
"I've got a great job here," Strong said. "I've got to get things done here."
"Each and every week I'm the topic of conversation on [ESPN]," Strong said with a laugh. "There hasn't been one week that I wasn't. Either they're ripping me or saying I've lost my team or saying something else."
Strong does have ties to coaching in the state of Florida. He began his career as a graduate assistant at Florida and had three stints as a Gators assistant, including serving as defensive coordinator from 2003 to 2009. He also recruited heavily in Miami and the rest of the state while coach at Louisville.
Strong makes more than $5 million annually at Texas, which is twice as much as Golden was reportedly paid by Miami, and he has the full support of new Texas president Greg Fenves and interim AD Mike Perrin.