That's according to an article in the Louisville Courier-Journal that has spun off articles on Forbes.com and USA Today.
The Courier-Journal recently interviewed Petrino's father, Bob Petrino, Sr., who told the newspaper that his son was doing okay financially but he misses coaching.
The article states that some UK fans have posted on local message boards they would welcome Petrino as a replacement to Joker Phillips.
The Courier-Journal quoted Petrino's father as saying "I just know this, that he's interested in Kentucky. He wants to stay in the SEC. That was his life's goal was to go to the SEC."
Petrino was fired by the University of Arkansas in April after being hurt in a motorcycle wreck that led to the discovery of his extramarital affair with his passenger, Jessica Dorrell, a 25-year-old athletic department worker who Petrino had personally hired.
Click here to read the Louisville Courier-Journal article on Petrino.