The Tennessean reports John A. Brown was to appear Wednesday to ask for his release.
The Board of Parole denied his last request in 2011, with Chairman Charles Traughber saying that the couple's killing was one of the most serious crimes there can be and noted that more than 450 people wrote to the board to oppose his release.
The Akemans were fatally shot as they returned to their home in Ridgetop following a performance of the Grand Ole Opry. Stringbean also performed on the TV program "Hee Haw."
The newspaper reports one parole board member will make a recommendation on Wednesday, but an official decision by the full board could take two weeks.
Country music entertainer Louis "Grandpa" Jones found the bodies the morning after the Akemans' were killed.
Jones' widow, Ramona Jones, was among the first on the scene and said Tuesday that she wrote a letter to the parole board in advance of the hearing asking that Brown be kept in prison.
"He still murdered two very innocent people," she said. "Don't let him out."