Burton said while Fleming has several verbal offers, UNC and N.C. State have shown the most interest.
According to the coach, UNC assistants Tommy Thigpen and Andre' Powell watched a small handful of Fleming's clips and drew up the offer almost immediately.
"For them to offer him during someone else's official visit shows something about C.J.'s ability," Burton said.
"C.J. is the hungriest football player that I've ever coached," Burton said. "He has a drive that no other kid I've ever coached had. Combine that with his physical skills and you have a star in the makings. He has all the physical tools. He's just a great kid to be around."
Fleming is ranked in Scout.com's initial Virginia 2007 Top 10 rankings.
The Tar Heel staff has developed a recent pipeline from Highland Springs to Chapel Hill. Offensive lineman Wyatt Hicks was a member of UNC's 2004 recruiting class and All-American linebacker Jarrell Miller signed with the class of 2006 this month.