League spokesman Greg Aiello confirmed the hearing schedule in an email to The Associated Press on Tuesday afternoon, about two hours after Payton's agent, Don Yee, said the coach and NFL were "trying to schedule a mutually convenient time for the proceedings" that would not interfere with people's plans for the upcoming religious holidays.
NFL commissioner Roger Goodell suspended Payton for all of next season. Loomis was suspended for eight games, Vitt for six, and the Saints were fined $500,000 and docked two second-round draft picks.
The unusually tough penalties stemmed from an NFL probe which concluded that from 2009-11 the Saints offered improper cash bonuses for big hits that either knocked opponents out of games or left them needing help off of the field.
Payton's suspension - due to start last Sunday - has been on hold pending his appeal, allowing him to get in a few extra days of work as he rushes to create a plan that's as detailed as possible for the Saints' 2012 season.
Beyond the punishment for Saints coaches and executives, the NFL still has to determine whether players who were involved in the bounty program will also be disciplined.
Speaking at a press event Tuesday for new NFL uniforms created by Nike, 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 Saints' offseason training program begins April 16. Thomas is hoping that, 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."
AP Pro Football Writer Howard Fendrich in Washington, D.C. and AP Sports Writer Brett Martel in New Orleans contributed to this report.