Lee made the comments at a forum alongside fellow Republican Gov. Matt Bevin of Kentucky about criminal justice reform at Belmont University's College of Law.
Don Johnson's execution is scheduled for May 16. Lee said he was "well underway" in making the assessment but also stressed that he's new to the job.
"For me, it's a thought process and something I've never had to consider in my whole life," Lee said. "The power is profound."
Johnson, 68, was convicted of murdering his wife, Connie Johnson, in 1984 by suffocating her in a Memphis camping center that he managed. He initially blamed the murder on a work-release inmate who confessed to helping dispose of the body and was granted immunity for testifying against Johnson, according to court documents.
Johnson's supporters have appealed to Lee's Christian faith, saying Johnson was redeemed by Jesus.
Kentucky hasn't executed any inmates in more than a decade, well before Bevin took office.
But the first-term governor says he has seen no need to wait until he's leaving office to grant pardons to prisoners, as is often customary for governors.
"I think if a person is worthy of being pardoned now, why should they have to wait four years?" Bevin said. "To me, that's crazy."
Both governors outlined criminal justice priorities and initiatives in an event co-hosted by Men of Valor and Right on Crime.
Bevin said he plans to create a sentencing integrity unit, saying mistakes just get made in sentencing.
He wondered out loud whether to grant prisoners re-entering society a one-year free pass for public transportation.
"I'm convinced something like that could work and that would go a long way at no real cost to anybody to fixing a problem that is a real problem," Bevin said.
Lee promised to examine sentencing guidelines in Tennessee but acknowledged it won't be easy.
"That's going to be really difficult because there are competing interests about what's fair," Lee said.
Lee has pursued a variety of criminal justice initiatives in his first year, including a bill to wipe away the $180 expungement fee that has already been passed. He has acknowledged that criminal justice reform will be a multiyear pursuit for him.
The forum was moderated by Belmont law school Dean Alberto Gonzales, the former U.S. attorney general.
Also in attendance was Matthew Charles, one of the first inmates released after federal sentencing reforms signed by President Donald Trump.
