The San Diego Union-Tribune reported Tuesday that Cooper was denied a hearing by a panel of appeals court judges. They were critical of the handling of Cooper's case by the trial judge, but still denied him a rehearing.
Disagreeing with the majority of the panel, Judge William Fletcher wrote a blistering dissent.
"The state of California may be about to execute an innocent man," Fletcher wrote.
Cooper's lawyer said he will ask the U.S. Supreme Court to hear the case.
Cooper, who has been on death row since May 1985, was convicted of killing Douglas and Peggy Ryen, their 10-year-old daughter, Jessica, and 11-year-old house guest Chris Hughes in Chino Hills, Calif.