The NFL Network and ESPN have reported Payton could meet with Parcells this week during owners' meetings in Florida about the possibility of taking over the team temporarily.
Parcells was a two-time Super Bowl winner with the New York Giants. He also was head coach for New England, the New York Jets and Dallas. He worked as a television analyst this past season after leaving the Miami Dolphins where he was vice president for football operations.
Payton will go on suspension April 1 and will miss the entire 2012 season for his role in the Saints policy of paying defensive players who inflicted injuries on opposing offensive players.
Other possible candidates reported to have received consideration include Saints offensive coordinator Pete Carmichael and new defensive coordinator Steve Spagnuolo, who had been head coach in St. Louis.