Saints spokesman Greg Bensel did confirm that Loomis was appealing his eight-game suspension and, separately, the team would challenge its $500,000 fine and loss of second-round draft picks this year and in 2013.
Vitt, suspended for six games, is doing the same. David Cornwell, representing Vitt as head of the NFL Coaches Association, confirmed the decision in an email to the AP.
Goodell last week announced the suspension of Payton, starting Sunday, for his role in connection with New Orleans' bounty system, which offered improper cash bonuses for big hits that either knocked opponents out of games or left them needing help off of the field.
The commissioner has said since the unprecedented penalties were announced that the Saints' coach would likely be allowed to continue working as his appeal was resolved. However, he added that the challenge would be expedited, indicating that Payton would not likely be able to add on much work time should his appeal be upheld.
Goodell also said at the NFL owners meetings this week in Florida that Payton could have some contact with the team but did not go into detail, and Payton indicated that he was still a little unclear about that, as well.
With all the uncertainty, Payton is trying to compress as much planning for the 2012 season into whatever time he has left at Saints headquarters this weekend.
The NFL could not immediately provide details on how Payton's decision to file an appeal on Friday would affect the timeline for the process to play out.
"The decision to appeal is for Sean Payton to make and announce as he deems appropriate," NFL spokesman Greg Aiello said. "If there are appeals, the commissioner will arrange for expedited hearings, as he stated at the league meeting."
The results of the appeal could affect whether Bill Parcells comes out of retirement to take over as interim coach while his former offensive assistant and protege is suspended.
Parcells has said he would consider coaching the Saints if asked. At a spring training game in Jupiter, Fla., on Friday, Parcells declined to answer questions about the possibility.
"I know better than that," Parcells said.
Payton and Loomis played golf with Parcells this week to talk to him about the team's predicament, and Parcells has told multiple media outlets that he would consider taking the Saints interim post to help his friend.
If the suspension is reduced, however, the Saints could decide it makes more sense to promote an assistant from the current staff.
There are also three strong candidates among Saints assistants to take over as interim coach: offensive coordinator Pete Carmichael, defensive coordinator Steve Spagnuolo and offensive line coach Aaron Kromer. Payton expressed confidence in the abilities of his own assistants to compensate for his absence, but also has voiced some misgivings about saddling those coaches with additional responsibilities.
Since his suspension was announced, Payton has been putting in long hours with his staff and that of Loomis as they try to lay out plans for the 2012 draft and season.
Loomis will be able to oversee the draft and handle other roster moves up until the season starts. Then, barring a successful appeal, he will serve his suspension for failing to put a stop to the bounty system in a timely way.
The NFL's investigation in New Orleans found that Payton initially lied to league investigators about the existence of a bounty program and instructed his defensive assistants to do the same.
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.
The NFL has said as many as 27 players also could be sanctioned for their role in the scandal, but it is not yet clear when that might happen, creating additional uncertainty for New Orleans and some teams that have signed former Saints defensive regulars as they tried to build their 2012 rosters.
DeMaurice Smith, executive director of the NFL Players Association, told the website Pro Player Insiders that the league hasn't turned over what the union would consider direct evidence of player involvement in a `pay to injure' scheme.
"If there is direct evidence of a `pay to injure' scheme implicating players or anybody involved," Smith said, "we are asking the league to turn over that information."