The 6-foot-3, 212-pound Stephens camped with the Wildcats in July. UK made a strong impression on the wide receiver/tight end prospect that has carried into August.
"He is staying in touch with their coaches," said the player's father, Wayne Stephens. "He really liked all of them when he was up there for their camp. He had a great time. What they've been doing now is talking about getting him back up there for one of their games. I think he'll wind up doing that, but we're not exactly sure when."
It could occur when his home state Gators make their way to Lexington on the weekend of Sept. 28.
"He saw that on the schedule and said that's one he'd really like to see," Wayne Stephens said. "He'd like to see those two teams up close."
Florida has also been recruiting Stephens, but has yet to issue a scholarship offer. He is also hearing from Florida State, although less frequently than other programs like UK, South Carolina, Vanderbilt, Iowa State and East Carolina.
He attended camp with the Gamecocks shortly after being at UK.
"He liked it," Wayne Stephens said of South Carolina. "They've been trying to get him up there for a while. He went to a half-day camp and spent the other time touring the campus and checking out the town."
Asked if his son has a favorite, Wayne Stephens said: "I don't know about that, but right now, Kentucky is up there pretty high with him. He likes what he's heard from them, and he liked the coaches and everything when he was up there. Plus, he's been talking about maybe going away from home for college so there will be less distractions, so that might be good for them."
Stephens is currently preparing for his senior season, which will get underway next week with a preseason scrimmage. He's looking forward to showing people what he can do now that he's back to full health. He had approximately 70 catches for 700 yards and eight touchdowns as a junior despite being hobbled by an Achilles injury for more than half the season.
According to his father, he was recently invited to play with the United States' Under-19 team in an all-star game in Dallas, Texas, following his senior season.
Kentucky is still seeking at least one additional receiver in its 2014 class. The Cats are also in strong with players like Braxton Berrios from North Carolina, Blake Bone from South Carolina and Dorian Baker of Ohio.