The news of Barnes' candidacy was first reported by 247Sports.
UCLA has made an aggressive push to land Barnes, and the two sides have had serious conversations, sources told ESPN's Chris Low. But Barnes also met with Tennessee athletic director Phillip Fulmer on Sunday night, sources said.
Barnes has been at Tennessee since 2015, and he was at Texas for the previous 17 seasons. He led the Volunteers to a share of the SEC regular-season title last year, and he had them as the No. 1 team in the country for several weeks this season. Tennessee's season ended in the Sweet 16 with a loss to Purdue.
Barnes, who was named the 2019 Naismith Coach of the Year on Sunday, signed a contract extension in September with Tennessee that runs through the 2023-24 season and paid him $3.25 million this season.Barnes' current buyout at Tennessee is $5 million.
UCLA fired Steve Alford on New Year's Eve and has been searching for a replacement for the past three months. The school has targeted Virginia's Tony Bennett, but sources told ESPN he's delaying any discussions until after the season. The Cavaliers play Texas Tech in the national championship game Monday night.
UCLA had discussions with Kentucky's John Calipari, but he signed a lifetime deal with the Wildcats last week. They also engaged in talks with TCU's Jamie Dixon, but the two sides could not come to an agreement on Dixon's $8 million buyout with the Horned Frogs.
Reports emerged earlier Sunday that Oklahoma's Lon Kruger had interviewed with UCLA, but Kruger released a statement on Sunday night denying any connection to the Bruins.
"I have not interviewed for the job at UCLA, nor have I had any contact with anyone from UCLA," Kruger said.
Wilbon: UCLA can still be a great head coaching job
Michael Wilbon says that UCLA can achieve great success again, especially with Jamie Dixon in talks to become the new head coach.