The interest between the school and Holtmann is reportedly mutual, said sources who spoke to the newspaper on the condition of anonymity.
Holtmann is one of several coaches being considered for the position, the report said.
Tennessee fired Tyndall on Friday after only one year with the program. Tyndall had met with the NCAA in November over concerns that the players at the school he formerly coached, Southern Mississippi, received impermissible benefits.
The NCAA had informed Tennessee it planned to impose violations on Tyndall in the near future.
Both coaches recently finished their first season with their respective schools. Holtmann went 23-11 with Butler, and led the Bulldogs to the NCAA tournament's third round.
Tyndall's Volunteers were 16-16 in 2014-15, finishing 7-11 in SEC play.
- Will Green