A list of unsigned orders issued Tuesday by the court shows Dunlap's petition to challenge his death sentence was denied.
It ends the last appeal he is guaranteed under the law, and clears the way for an execution date to be set, the Denver Post reported Tuesday.
Dunlap, now 38, was 19 in 1993 when he killed four employees of a Chuck E. Cheese restaurant in Aurora, Colo., his former employer. Sylvia Crowell, 19, Ben Grant, 17, Colleen O'Connor, 17, and restaurant manager Margaret Kohlberg, 50, died, and a fifth employee was gravely wounded but survived.
Police said Dunlap was upset over being fired from the restaurant.
Dunlap is Colorado's longest-serving death-row inmate and could be the first to be executed in the state since 1997, the newspaper said.