Payton, speaking to reporters at the NFL meetings in Florida, said he wanted to meet with Parcells, the former two-time New York Giants Super Bowl winning coach, to discuss the possibility of him filling in as coach.
"He's a Hall of Fame head coach," Payton said.
"I would say there are probably some things set up in the framework of our program that would be exactly how he would have set things up had he been the head coach here in '06, so there is some carryover that way."
Parcells, 70, worked as head coach of the Giants, New England Patriots, New York Jets and Dallas Cowboys before retiring in 2006.
He was executive vice president of football operations for the Miami Dolphins from 2008-10 and now works as a television analyst.
Payton said he expected to return as the Saints' coach in 2013 and would decide in the next two or three days whether to appeal the ban over his role in the Saints' "pay for pain" bounty scandal.
Payton has until April 2 to decide whether to appeal. NFL Commissioner Roger Goodell has said he would probably allow Payton to continue working during an appeal.
"I think the commissioner has done a great job communicating with us throughout this process," Payton said.
"He's made it clear and for good reason...the idea of something with this magnitude is an important issue that he wanted to address."
Goodell announced last week that Payton had been suspended for one season after the NFL took a dim view of the revelations that the Saints had been rewarding their players for deliberately injuring their opponents.
Former defensive coordinator Gregg Williams, now with the St. Louis Rams, was suspended indefinitely.
Saints general manager Mickey Loomis was slapped with an eight game suspension and assistant head coach Joe Vitt was suspended for six games.