Kentucky offered months ago and Louisville may be on the verge of doing the same. Others such as Alabama, Boston College, Notre Dame and Tennessee are also expressing an early interest.
Ulinski, who is the grandson of former Wildcat standout Harry Ulinski, visited the hometown Cardinals on Tuesday.
"I went over there to watch them practice," said Ulinski. "That's the first time that I have been able to see them in action like that."
During his visit, Ulinski visited with U of L defensive line coach Mark Nelson and observed much of the 11-on-11 portion of the practice just a few yards behind the offensive huddle.
"That was a lot of fun," he said. "It was good to see how they do things. I liked it. It made me feel like I could get real close with the players. They made me feel like they really want me there."
Primarily a defensive tackle throughout his high school career, which included a couple seasons with current Cardinal Aundre Henderson, Ulinski said that both the Cardinals and Wildcats are recruiting him as such.
"UK told me that they want me as a defensive lineman, but that if there wasn't a spot for me that I could play on the offensive line and that's fine with me and Louisville's talked about playing on the defensive line."
Due to the family ties with Kentucky, many consider him a near lock for the Wildcats.
"People are going to say that," said Ulinski. "My family are all UK fans and we go up to the games, but no one is pressuring me to go there. Everyone just wants me to go where I feel comfortable."
Ulinski, who will attend the Kentucky spring game on Saturday and has plans to attend camps at both U of L and UK, hopes to have his college choice made before taking the field this fall.
"I'd like to do it before the start of the season," he said. "I'm going to go to a few camps and then see what happens."