Barnes has reportedly been "mulling" over his options.
The Bruins athletic department has had three months to find a head coach, a task not deemed too hard for most college basketball programs, let alone one with the pedigree of UCLA.
On Monday morning, several sources reported that Barnes met with Fulmer to discuss a counteroffer.
During halftime of the national championship game between Texas Tech and Virginia, ESPN's Chris Low first reported that former Texas Longhorns coach Rick Barnes made a decision to remain as Tennessee's head basketball coach despite interest from UCLA.
"I am incredibly humbled and honored to become the head coach at UCLA", Cronin said in a statement.
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UCLA officials were in Knoxville over the weekend and made Barnes a five-year offer.
The Volunteers have steadily risen since Barnes took over for Donnie Tyndall, going from a 15-19 record in his first season to an SEC power and NCAA tournament 2-seed this season. When Barnes took over the Tennessee program he was tasked with rebuilding the culture after Donnie Tyndall was sacked following the NCAA ten year show-cause penalty levied against Tyndall. Calipari eventually told school officials he wasn't interested before accepting what amounted to a lifetime contract to remain with the Wildcats. Barnes would come slightly cheaper at $5 million, per 247 Sports.
Barnes' overall coaching record is 692-364, with stops at George Mason, Providence, Clemson and Texas before Tennessee. If he does depart, Tennessee Athletic Director Phillip Fulmer will have to fill both the men's and women's basketball coaching jobs after the firing last month of Holly Warlick, who struggled to continue the success of the legendary Pat Summitt. One of the things Barnes has always put a premium on is his assistants and staff being taken care of financially and providing as much security for them as possible, which was paramount in his talks with UCLA and ultimately his decision to stay at Tennessee.
So now UCLA is moving into the next phase of their search with Barnes as the apparent favorite.