These two gentlemen could be meeting Tuesday. (US Presswire)

Last week, the four players suspended for their roles in the Saints Bountygate won an appeal from the courts, forcing commissioner Roger Goodell to reconsider the penalty to Jonathan Vilma, Anthony Hargrove, Will Smith and Scott Fujita.

On Monday, the NFLPA sent the NFL a letter detailing the steps Goodell needs to take before issuing another punishment. The league sent the union its own letter, saying Goodell would be willing to meet with any of the four players on Tuesday before deciding a course of action.

And it sounds like Vilma will take Goodell up on his offer.

That’s the word from NFL.com’s Albert Breer, who reports that a source close to Vilma said that the Saints linebacker (who was placed on the PUP list Monday) wants to meet with Goodell “to discuss the discipline as the process is re-opened in the Saints' bounty case.”

Vilma reportedly previously had planned to meet with Goodell on Aug. 23, but apparently, pre-existing conditions could not be agreed to by both sides (UPDATE: obtained by CBSSports.com's Mike Freeman, here's the backstory on why the meeting between Vilman and Goodell never happened).

Breer also reports that if the players believe Goodell’s new discipline is still unfair, they’ll appeal. That appeals process would be overseen by a third party and not the NFL commissioner.

UPDATED (1:35 p.m. ET): Via CBSSports.com's Mike Freeman, here's the NFL's statement on the report.

"Each player suspended in the Saints bounty matter has declined multiple opportunities to meet with league representatives to present information. We have reminded each of those players that we remain willing to meet with them prior to the commissioner making the determination called for by the CBA Appeals Panel. We intend to conduct any such meetings that are scheduled per our normal process under the CBA."

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