Muhammad is scheduled to die by lethal injection Nov. 10 at a Virginia prison.
Attorneys for the 48-year-old have said they planned to file the appeal Tuesday. They asked Gov. Timothy M. Kaine for clemency last month.
Muhammad is to be executed for the slaying of Dean Harold Meyers at a Manassas, Va., gas station during a three-week killing spree in October 2002 that left 10 dead in Maryland, Virginia and the District of Columbia.
Muhammad and his teenage accomplice, Lee Boyd Malvo, were also suspected of fatal shootings in other states, including Arizona, Louisiana and Alabama. Malvo is serving a life sentence in prison.