The NFLPA filed a grievance, claiming Goodell cannot punish players for conduct prior to the current collective bargaining agreement, which took effect Aug. 4, according to ESPN.com.
The grievance was filed with arbitrator Stephen Burbank. The law professor at the University of Pennsylvania was selected to serves as the "system arbitrator" for the NFL and the union.
"In connection with entering into the 2011 CBA, the NFL released all players from conduct engaged in prior to the execution of the CBA, on August 4, 2011," the grievance said, ESPN reported.
The union claimed that "only the system arbitrator -- and not the commissioner -- has authority under the CBA to punish players for their alleged participation" in the bounty program.
Also, the union is upset that it never received the evidence from the NFL's investigation and the NFLPA did not recommend discipline for any of the players, ESPN reported.
On Wednesday, Goodell announced that two current and two former Saints players were suspended. Saints linebacker Jonathan Vilma was suspended for 12 games, Packers Anthony Hargrove eight games, Saints defensive end Will Smith four games and Browns linebacker Scott Fajita three games. All four were with the Saints during the 2009 season.
The Saints bounty scandal already has earned, among others, Saints coach Sean Payton a season suspension, general manager Mick Loomis eight games and former defensive coordinator Gregg Williams an indefinite suspension.