Wide receivers Tim Brown, Cris Carter and Andre Reed also are on the list that was released Saturday.
Parcells, Brown, Carter and Reed will be considered for induction when the Hall's selection committee meets in Indianapolis next month. A finalist must receive 80 per cent of the vote to be enshrined.
Parcells also was a finalist in 2001 and 2002. He became the Dallas Cowboys coach in 2003 and retired again three years later, beginning the five-year waiting period to be considered for the Hall again.
Former Kansas City guard Will Shields also made the list of finalists in his first year of eligibility.