"I don't agree with that," Goodell said Monday at the opening of an NFL pop-up store featuring new team apparel. "At the end of the day, these are management decisions that (owner) Tom Benson has to sign off on. He'll get recommendations, from Sean and (general manager) Mickey (Loomis), I'm sure, and others, and make his determination.
Payton, who received a season-long suspension that he's appealing, has acknowledged talking with former NFL coach Bill Parcells about taking his place on an interim basis.
"If it ends up being Parcells, and they've gone through the full process, that's their decision," said Goodell, who said last week that the Saints would have to interview minority candidates in accordance with the league's Rooney Rule before making an outside hire. "They need to make those decisions."
Goodell added: "Bill's a great coach, and he will add a lot of personality and intrigue, and he's as competitive as they get. I'm sure he'll do a great job."
Parcells has said he would consider coaching the Saints if asked. Payton and Loomis played golf with Parcells last week to talk to him about the team's predicament.
The Associated Press contributed to this report.