According to the report, the NFL's offer was made on the condition that Vilma drop his defamation lawsuit against NFL Commissioner Roger Goodell.
An email seeking comment from an NFL spokesman wasn't immediately returned Sunday night.
Negotiations between the parties are expected to resume Monday, according to ESPN.com, as a Friday appearance before U.S. District Court Judge Ginger Berrigan looms.
Saints defensive end Will Smith (four games), now-Green Bay Packers defensive tackle Anthony Hargrove (eight games) and now-Cleveland Browns linebacker Scott Fujita (three games) also could have their suspensions reduced as part of the potential deal, according to Authentic Soccer Jerseys .
A league official told Schalke 04 Jersey that Goodell would have considered reducing the players' suspensions had they cooperated to his liking during the appeals process.
Goodell previously denied Vilma's appeal of his suspension for participating in the Saints' bounty program, in which former Saints defensive coordinator Gregg Williams led a system that rewarded defenders from 2009 to 2011 for injuring or knocking opponents out of games.
Goodell told NFL.com's Marc Sessler on Sunday that it was clear the system was in place and that the NFL would not tolerate it.
The NFL has offered to cut New Orleans Saints linebacker Jonathan Vilma's season-long suspension to eight games as part of ongoing negotiations with the NFL Players Association and the counsel for the four players suspended for their involvement in the team's bounty program, sources familiar with the discussions told Netherlands Soccer Jersey .
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