Despite a solid résumé at multiple big programs, Barnes would still likely be a somewhat disappointing hire for UCLA fans yearning for the program's days as one of the elite programs in college basketball.
Fulmer said he was grateful to both Barnes and his wife, as well as the "university leadership, which stepped up to show Rick how much he is valued and appreciated". "Our commitment to basketball has never been stronger, and we're all excited for the future as we move forward".
However, UCLA has traditionally been one of the best jobs in the country, and the school could offer a huge financial package to secure Barnes.
Most importantly to UCLA, Barnes would be very interested in heading west if offered the chance per the Los Angeles Times' Ben Bolch.
Sunday, Barnes became the first Tennessee men's basketball coach to win the Naismith Coach of the Year Award.
The statement came after reports that linked Barnes to the coaching vacancy at UCLA. Barnes finalized his decision to stay as the Vols' coach on Monday night after Tennessee countered with a new deal that was in the neighborhood of what UCLA was offering.
Barnes, 64, is highly respected within the coaching fraternity but already is as old as legendary UCLA coach John Wooden was when he retired in 1975.
The same source told ESPN that Barnes "loves living in East Tennessee and loves the people in Tennessee".
Barnes was paid $3.25 million this season, according to USA Today's salary database, after agreeing to a contract extension that included $100,000 annual raises.
UCLA also had interest in Texas Christian's Jamie Dixon, but the school elected to pursue other options last week after reportedly electing to not pay the $8 million buyout of his contract.