Defense attorneys would like to convince the judge to let them appeal some rulings before the trial begins for Antonio Jones and Lacy J. Barnard.
A trial date has not been scheduled.
District Attorney Ashley Wright has said will oppose any pretrial appeal.
Mr. Jones, 29, and Ms. Barnard, 20 pleaded not guilty in Richmond County Superior Court to several charges, including capital murder.
Investigators contend they are responsible for the deaths of one of two men lured to a remote area near Brickyard Pond Road and Gordon Highway on March 27, 2007. Both men were robbed and shot repeatedly with a shotgun. One victim survived, but 23-year-old Eladio Gonzalez was killed.
Because they face death penalty trials, Mr. Jones and Ms. Barnard will be tried separately. Both have been held without bond since their arrests the day after the victims were found.
A third person arrested in the case, 55-year-old Ronald E. Banks, died of cancer in March 2008.