Davis' attorneys are expected to argue at 1 p.m. in the 11th U.S.
Circuit Court of Appeals that their client is innocent and should be granted a new trial.
Legal observers say it's an extraordinary effort to earn a re-hearing of evidence in the almost two-decades-old case after every court that has heard it refused to grant a new trial.
Davis' attorneys say affidavits from seven witnesses who fingered Davis as the shooter but later changed or were unsure about their testimony are strong evidence he is innocent.
Both the Georgia and U.S. Supreme Courts have refused to grant a new trial based on the affidavits.
Attorneys for the state argue Davis is not eligible for a new trial because a federal court already rejected a similar request based on the same evidence, and the 11th U.S. Circuit Court upheld that ruling in an earlier appeal.
Davis was convicted in 1991 for shooting MacPhail in a Burger King parking lot in Savannah. The officer, then 27, was working off-duty as a security guard and was responding to the cries of a homeless man being pistol-whipped near the restaurant when he was gunned down.
Davis has come within hours of lethal injection three times in the past two years. Additionally, the Georgia Board of Pardons and Paroles has twice denied Davis' pleas for clemency