Goodell spent six hours hearing appeals, meeting separately with Saints representatives, general manager Mickey Loomis, assistant coach Joe Vitt and finally Payton at NFL headquarters. Goodell's decision on the appeals could come as early as Friday, but it's more likely to happen next week.
Payton was rushed into a black van following the meeting and didn't stop to talk to reporters.
Lawyer David Cornwell, who represents Vitt, said Payton went in to see Goodell after Vitt's 90-minute session with the commissioner.
Cornwell said Vitt understood he had to be held accountable, but they wanted to convey that the coach didn't participate in a strategy to injure players.
"I thought the commissioner was extremely receptive," Cornwell said of the meeting.
Asked if he believed his six-game suspension would be reduced, Vitt said: "I have no feel for that."
"The commissioner's got a tough job," he added. "I've worked hard to earn the respect of my players, and now I want to earn his respect."
Goodell suspended Payton for all of next season for his role in the bounty system. Loomis was suspended for eight games, and the team was fined $500,000 and docked two second-round draft picks.
The league informed the Saints at the start of the playoffs that it was reopening its bounty investigation. Cornwell said Loomis and Payton then told Williams: "There's no place for this in this organization or this league."
However, in its statement last month announcing the penalties for team officials, the NFL said the GM and coach made only "cursory inquiries" into the possible presence of a bounty program.
Payton twice apologized for his role in the bounty program, saying he takes "full responsibility" for a system that operated for three years under his watch.
Beyond the punishment for Saints coaches and executives, the NFL still has to determine if players who were involved in the bounty program also will be disciplined. The NFL has said as many as 27 players could be sanctioned for their role in the scandal.
Follow Steve Wyche on Twitter @wyche89.
The Associated Press contributed to this report.