The 11th Circuit Court of Appeals in Atlanta is to hear Davis' request for a new trial Tuesday, The Atlanta Journal-Constitution reported Monday.
Davis, who was sentenced to die after being convicted of killing Savannah police officer Mark MacPhail, has come close to execution three times in the last 17 months, the newspaper reported.
Davis' lawyers say a new trial is warranted because seven of nine witnesses have recanted or are uncertain of their testimony about MacPhail's killing in 1989 in a Savannah fast-food parking lot.
Davis' case previously has been heard, and his conviction upheld, by state and federal courts, including the U.S. Supreme Court. His lawyers, however, say it would be "constitutionally intolerable" to execute Davis without examining the new evidence, the newspaper reported.