The news was first reported by Kentucky Sports Radio.
Stoops, Florida State’s defensive coordinator, is the younger brother of Oklahoma coach Bob Stoops and Sooners defensive coordinator Mike Stoops.
Mark Stoops was an assistant at South Florida, Wyoming, Houston and Miami before joining Mike Stoops’ Arizona staff in 2004.
He became Florida State’s defensive coordinator in 2009; while at FSU, he coached twice against Bob Stoops’ Oklahoma teams, which beat the Seminoles 47-17 in Norman two years ago, and 23-13 in Tallahassee, Fla., last season.
Asked about the possibility of his brother accepting the Kentucky job at Monday’s news conference, Bob Stoops didn’t say much.
“I’m sure it’s a good job,” he said. “All jobs are good jobs, for the most part. As long as they’ve got a little money to help the football team.”