Gary Wayne Rodgers, 46, had no address in Lexington, said deputy coroner Steve McCown.
Witnesses saw Rodgers around 12:30 p.m. EST in the parking lot on the west side of Rupp, where the Kentucky men's basketball team plays its home games.
Minutes later, witnesses told police Rodgers was on fire, McCown's report said. Bystanders put out the flames with a fire extinguisher before paramedics arrived, but Rodgers died at the scene, McCown said.
An autopsy was scheduled for Sunday in Frankfort.
McCown would not speculate on whether Rodgers set himself on fire. However, he said foul play was not suspected.
McCown was investigating whether Rodgers was covered with any accelerants, like gasoline. He said the burns were not centralized in one part of Rodgers' body.
``He was just burned all over,'' McCown said.