One of the people also says New Orleans linebacker Jonathan Vilma expects to play at Tampa Bay on Oct. 21 while his appeal is pending. The people spoke to The Associated Press Friday on condition of anonymity because the appeals were filed as private documents with the league.
NFL spokesman Greg Aiello confirmed Friday that all four players had filed appeals, but said the league would decline comment on the substance of those documents.
This marks the second round of appeals by the players.
About a month ago, a three-member appeal panel created by the NFL's collective bargaining agreement vacated initial disciplinary rulings handed down by Goodell. Then Tuesday, the commissioner upheld his initial suspensions of Vilma and Saints defensive end Will Smith, and revised his suspensions of Cleveland linebacker and former Saint Scott Fujita and free agent defensive lineman Anthony Hargrove.
Vilma has been on the Saints' physically unable to perform list while continuing his comeback from off-season surgery on his left knee, but may be activated after the first six weeks of the regular season. Goodell said Vilma could be paid for his time on New Orleans' PUP list.
New Orleans has a bye this week, then the Saints could activate Vilma next week, if he is healthy enough to play. When Vilma was first place on the PUP list, Saints interim coach Aaron Kromer said the goal was to have Vilma back in the lineup by Week 7.
"Excited to get Vilma back out there on the field," Saints linebacker Scott Shanle said in a text to the AP Friday. "Played a lot of football with him and know how much he brings to the team and inside our defensive huddle on game day."
Barring a successful appeal, Vilma will remain suspended for the season, while Smith will remain suspended four games. Hargrove's suspension was reduced from eight to seven games and Fujita's was cut from three games to one.
In effect, Hargrove now faces a two-game ban because his initial eight-game suspension was reduced by one and he was given credit for five games missed as a free agent after he was cut by Green Bay in the preseason.
The new appeals are only the latest of many manoeuvrs in a contentious months-long back-and-forth involving the players, the NFL Players Association and the league office.
Vilma has a related defamation case pending against Goodell in federal court in New Orleans.
In addition, Vilma and the NFLPA, which is representing the other three players, could ask U.S. District Judge Ginger Berrigan to revisit their earlier legal challenge of the suspensions.
The union and Vilma would have to refile those requests with Berrigan, who placed the matter on indefinite hold when the three-member NFL appeal panel vacated the initial suspensions on technical ground and informed Goodell that he had to clarify his basis for the punishment.
The panel, which did not address the merits of the investigation, said it needed to be clear that Goodell's disciplinary decisions in the Saints' cash-for-hits pool pertained exclusively to conduct detrimental to football, and not salary cap violations, which would have to be handled by an arbitrator other than the commissioner.
Berrigan has stated that she found the NFL's disciplinary process unfair and that she would be inclined to grant Vilma at least a temporary restraining order if she believed she had jurisdiction on the matter.
However, Berrigan also has stated that she is hesitant to rule until she is certain the players have exhausted all possible remedies available to them through the NFL's labour agreement. She has further stressed that all parties would be wise to settle the matter out of court, but a federal magistrate has had little success getting meaningful settlement talks moving.
The four players were implicated in what the NFL said was a bounty pool run by former Saints defensive co-ordinator Gregg Williams and paid improper cash bonuses for hits that injured opponents. The players have acknowledged a pool but denied they intended to injure anyone. Goodell has been unmoved by the players' distinction regarding intent, outlining several instances in which Williams made notations of player rewards due for hits that knocked opponents out of games.
Williams, now with St. Louis, has co-operated with the league's investigation but is currently suspended indefinitely. Saints head coach Sean Payton is suspended for the season, general manager Mickey Loomis for eight games and assistant head coach Joe Vitt six games. They were punished separately from the players and all are serving out their punishment.
By contrast, the players and their union have put up intense resistance for the past half-year with no sign of letting up.
Even after his suspension was reduced this week, Fujita was harshly critical of Goodell, calling the "condescending tone" of his disciplinary letter unproductive, accusing the commissioner of misusing his power and questioning Goodell's record on player safety.
"The commissioner says he is disappointed in me," Fujita said Wednesday. "The truth is, I'm disappointed in him."