"I expect we'll do it before the end of the week," Goodell said Tuesday at the unveiling of the league's new Nike-designed uniforms at a film studio in Brooklyn.
Payton, New Orleans general manager Mickey Loomis and assistant coach Joe Vitt were suspended for their roles in the team's bounty program, which offered improper cash bonuses for big hits that either knocked opponents out of games or left them needing help off of the field.
Payton was suspended for the upcoming season. Loomis received an eight-game suspension, and Vitt was suspended for six games. The Saints organization was fined $500,000 and had second-round draft picks this year and next taken away by the league as part of the punishment.
Donald Yee, Payton's agent, released a statement later Tuesday that did not rule out a meeting with the commissioner later in the week but said, "We've just heard from the league office today for the first time, and at the moment, we are trying to schedule a mutually convenient time for the proceedings to occur, particularly given the upcoming Good Friday, Passover and Easter holidays."
Payton's suspension originally was to have started on Sunday, but it's been on hold pending his appeal.
After Saints coaches and executives, next to be determined is whether players who were involved in the bounty program will also be disciplined.
Goodell said the NFL met with the players' association representatives on Monday to discuss the league's investigation of the Saints.
"We shared more information with them so they're up to speed," he said.
Goodell added that he expected to speak with NFLPA chief DeMaurice Smith again as soon as Wednesday.
"I hope to be able to make some decisions soon," Goodell said.
"I believe in getting as much information as possible," he said. "We respect the players. This is important because it's a player safety matter. We think that we need to get some input from them."
"We're players. We're going out there to make plays. That's what the game is about," he said. "You play defense, your job is to tackle.
"They can say they put a bounty out on me when I got knocked out against San Francisco in the playoffs. You can say they put a bounty out on me. Who knows? But they're just targeting us right now," he said. "But I'm not faulting the guy that hit me. It's the nature of the game. That happens."
"We all respect each other so much," he said. "We all know how hard it is. It really surprised me that guys would want to try to intentionally hurt somebody. This is a fraternity. There's so few of us that do it. The average life expectancy is three years in the NFL or something like that.
"It would shock me if people were trying to intentionally hurt people."
Thomas said he has not spoken with Vilma or any of his other teammates on defense.
"They probably got a lot on their plate as it is. It's not my business to jump in," he said.
Goodell has said he would be fine with Parcells stepping in. Thomas liked the idea, too.
"I mean it would be great. That's somebody coach Payton always talked about in meetings, admired him. He seemed like a great coach. I never played underneath him, but I learned a lot about him. I heard a lot about him. He seems like a great guy," Thomas said.
"I know we would love to have him if it happens, but we would prefer Payton to be there with his team, to lead us on the way he's been doing."
The first organized team activity for the Saints is April 16. Thomas is hoping no matter what happens, the bounty scandal will be settled by then.
"Hopefully, this doesn't keep lingering on," he said. "You don't want this to linger on while we're preparing for a season. You want to make sure everything is focused on one thing: Trying to get to that Super Bowl."