Vilma has been suspended for the 2012 season for his role in the Saints bounty program, which he adamantly has claimed did not exist. Citing anonymous sources, ESPN.com reported the league offered Vilma an eight-game suspension if he would drop his defamation lawsuit against NFL Commissioner Roger Goodell.
"No such settlement offer has been made," NFL spokesman Greg Aiello said Monday. "We will continue to respect the court proceedings on this matter and have no further comment at this time."
A judge has ordered the league and Vilma's representatives to hold confidential settlement talks. A person familiar with those talks told The Associated Press he had "not heard anything that concrete from anyone at the NFL" regarding cutting Vilma's suspension to eight games.
The person, who spoke anonymously because the talks are private, added that he was aware of no offers from the league at all.
It is uncertain if Vilma would consider such a reduction in the suspension as he fights to have it overturned completely.
Vilma's teammates were pleased by the possibility of the linebacker playing this season.
"Even the thought of getting him back is exciting for us and I really hope that this thing works out in his favour, because we all have his back 100 per cent. We support (him)," safety Malcolm Jenkins said.
Peter Ginsberg, Vilma's attorney, did not immediately respond to a request for comment. But he filed a motion in U.S. District Court in Louisiana on Monday on behalf of his client, seeking "judicial attention" to comments Goodell recently made.
The filing claims "the NFL breached its CBA obligation to produce all evidence to be considered by the arbitrator in a 'conduct detrimental' proceeding; Goodell acted in an impermissibly biased manner; and, Goodell created and permitted a process tolerated neither by the CBA nor by federal law."
According to the Louisiana filing, Goodell "has revised the allegation" against the Saints to engaging in a program that rewarded players for clean plays "that did not involve designated specific opposing players for injury."
Vilma is one of four players suspended in the bounty scandal. Teammate Will Smith, a defensive end, got four games, while DE Anthony Hargrove, now with Green Bay, was docked eight games. Linebacker Scott Fujita, now with Cleveland, was suspended for three games.
Saints coach Sean Payton, like Vilma, was suspended for the entire season.
AP Sports Writer Brett Martel in New Orleans contributed to this story.