Over the coming weekends, the 6-foot-3, 260-pound Cuney will make junior day trips to Texas (Feb. 23) and Texas A&M (March 2).
The 2014 prospect has been picking up interest from several schools.
"It's too exciting," Cuney said. "I know this week is going to go by slowly for me. That's just how it is. The weekend can't get here fast enough."
Cuney ventured to College Station, Texas, on Saturday to take a tour of the A&M campus with his family and a friend of his who graduated from Texas A&M. Cuney said that he didn't seek out any coaches while he was on the trip since he'll get a chance to take in the football side of things on March 2.
But he liked what he saw while in Aggieland.
"All the people are like super friendly," Cuney said. "That's the nice part about it. They have their little 'Howdy' thing and they're real friendly. They really welcome you in."
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As for Texas, Cuney said head coach Mack Brown and offensive line coach Stacy Searels stopped by Jasper in recent months.
"Searels and Coach Brown have come down," Cuney said. "I couldn't believe that. ... They introduced themselves. I know Coach Searels and we're pretty cool."
Cuney said he liked the Longhorns as a child.
"Texas was my favorite team growing up," he said. "I loved the 'Hook 'em' thing. Something about that that I love. My town loves Texas."
The three-year varsity starter at center was part of a 9-3 Jasper squad that made the Texas Class 3A playoffs before falling to eventual Division II state champion Navasota. In addition to Texas A&M, he has interest from LSU, Florida State, UCLA and Oklahoma State.