Workman was convicted for the 1981 shooting death of Memphis Police Lieutenant Ronald Oliver.
His defense team is also reviewing revised execution rules released by the state to decide whether they should be challenged in court.
Workman has two appeals pending before the 6th United States Circuit Court of Appeals.
His lawyers requested the stay of execution claiming he was convicted on perjured testimony and that the state withheld evidence that would have established Workman's innocence.
He has twice been within hours of execution when courts stepped in to spare his life.