NEW YORK (Reuters) - National Football League (NFL) commissioner Roger Goodell said he hoped to wrap up the New Orleans Saints' "bounty" affair after meetings this week with representatives of the NFL Players Association.

Goodell, who attended the opening of an NFL store in midtown Manhattan on Monday was scheduled to meet with officials of the NFLPA later in the day.

Besides talks with the NFLPA about possible punishment for players that played a role in the scandal over bonuses paid for hits that knocked opponents out of games, Goodell also has four appeals to hear this week against discipline he laid down for Saints officials.

"I think we all need to move forward," Goodell told reporters.

The league already has levied punishments against the Saints ($500,000 and two second-round draft picks), general manager Mickey Loomis (eight games), coach Sean Payton (one year), assistant Joe Vitt (six games) and former defensive coordinator Gregg Williams (indefinitely).

All but Williams have filed appeals.

Goodell said, he was hoping to get a recommendation from the NFLPA on how the league should proceed regarding certain Saints players.

The pay-for-pain scheme is of major concern to the NFL which is worried about safety issues following a series of lawsuits from former players relating to concussions.

"We've given the NFLPA two of our confidential reports, which we've shared with our clubs...and we'll have the meeting today," said Goodell. "Hopefully they'll get some more information, (and) we'll get a recommendation from them."

The union's position has been that it was not the NFLPA's place to make a recommendation on sanctions. More than 20 Saints players were cited in the league's 50,000-page report from an investigation that lasted three years.

Players union chief DeMaurice Smith and the union's legal team met with Saints quarterback Drew Brees, defensive end Will Smith and ex-Saints linebacker Scott Fujita last month in Florida to gather more information.

The union has also hired outside counsel to handle the case, and told players that criminal charges were also a remote possibility, the NFL Network said.

Goodell defended the harsh discipline he has already meted out.

"For three years, they (Saints) denied this was going on," said Goodell. "It's clear it was going on and that's one of the reasons the punishment is harsh.

"From our standpoint, we want to find out (during the appeal) if there's information that we're not aware of and take that into consideration and we'll deal with it from there."

(Reporting By Larry Fine in New York; Editing by Steve Keating)