(Reuters) - New Orleans Saints quarterback Drew Brees and former team mate Scott Fujita accompanied union officials to meet with the NFL on Monday as the league considers possible player punishment over the "bounty" scandal.

Brees, who has not been linked to the controversial rewards system, and Fujita attended the meeting at NFL offices in New York as they are both members of the union's executive council.

They were joined NFL Players Association Executive Director DeMaurice Smith and President Domonique Foxworth for a meeting in New York, according to a report on the league's website.

The Saints franchise and its coaches have already received stiff penalties over the scheme that paid bonuses to individuals for knocking opponents out of games but players have yet to face any punishment.

The NFL has said that between 22 and 27 Saints players were involved in a bounty program that financially rewarded players for hurting opponents from 2009 to 2011 and that fines and bans were possible.

Fujita, a linebacker who spent four seasons with New Orleans before joining the Cleveland Browns in 2010, is one of the central figures in the investigation, according to the report.

On March 2, the NFL said Saints players were involved in the illegal "bounty" system and three weeks later came down hard on the club and its top coaches.

The Saints were fined $500,000 and stripped of two draft picks while head coach Sean Payton, who won a Super Bowl with the team in 2010, was suspended for the 2012 NFL season.

Saints General Manager Mickey Loomis was banned for eight games, assistant head coach Joe Vitt for six games and former Saints defensive coordinator Gregg Williams has been suspended indefinitely for his role in the scandal.

(Reporting by Larry Fine in New York; Editing by Frank Pingue)