"I think I'm ready for the next level, but I wasn't happy with the input I was getting from NBA teams," Cockburn said ahead of Tuesday's NCAA deadline for players to withdraw from the NBA draft and maintain college eligibility. "I didn't want to settle. I'm going to return for another year, raise my game and improve my draft stock."
Cockburn entered his name in the transfer portal last week and said he is still deciding where to play next season.
"I'm pretty much open. There's a possibility I return to Illinois and a possibility I don't," he told ESPN. "I want to make a quick decision as soon as possible. I don't want to go back and forth. I'm going to take some visits, but I'm not sure where."
Cockburn pointed to assistant coach Orlando Antigua leaving Illinois to become an assistant at Kentucky as one reason he decided to explore transferring.
"He's the reason I went to Illinois," Cockburn said of Antigua. "When he left along with Chin Coleman, I decided to go in the portal to leave my options open.
"Kentucky? It's a serious option. Antigua is my guy. I'm going to consider them, but there [are] a lot of schools. I wasn't really focused on that while I was in the NBA draft. Now I can take my time and evaluate it better."
A 7-foot-1 big man born in Kingston, Jamaica, Cockburn was named first-team All-Big Ten and a second-team All-American after a breakout season in which he averaged 17.7 points, 9.5 rebounds and 1.3 blocks in 27 minutes per game, shooting 65.4% from the field.
Cockburn was the No. 1 pick-and-roll finisher in college basketball last season, according to Synergy, leading the country with 78 slam dunks. He is one of the most physically imposing players in the college game with his 7-4 wingspan, 9-3 standing reach and 298-pound frame.
He said the feedback from NBA teams was that they want to see more of his perimeter skill, be it his jump shot or passing ability.
"NBA teams are going to see my midrange game next year and my playmaking," Cockburn said.
Jonathan Givony is an NBA draft expert and the founder and co-owner of DraftExpress.com, a private scouting and analytics service used by NBA, NCAA and international teams.