Vilma, who made the choice and decision, originally had been scheduled to meet with Goodell on Tuesday.
The other three players alleged to have been involved in the Saints' bounty scandal still will meet with Goodell on Tuesday in New York, a source with knowledge of the meeting told ESPN.
Vilma; Will Smith of the Saints; Scott Fujita, a former member of the Saints now with the Cleveland Browns; and Anthony Hargrove, a former Saints player who is a free agent, are facing possible renewed suspensions.
The original suspensions of those four players were vacated Friday by a three-member appeals panel. Vilma originally was suspended for the season, Hargrove for eight games, Smith for four games and Fujita for three games.
The NFL on Thursday issued a statement to clarify the ruling from the internal appeals panel under the collective bargaining agreement.
"In light of some confusion surrounding the ruling of the CBA Appeals Panel, it is important to understand what the panel did and did not rule," the league says. "The panel did not overturn the suspensions and did not say Commissioner Goodell overstepped his authority."
Ginsberg disagreed with the league's take.
"It is interesting and illuminating that it took the NFL almost one week to develop a publishable rationalization of the Appeals Board decision," Ginsberg said in a statement. "Contrary to the NFL's media statement, the Appeals Panel voided the suspensions -- it did not 'put the suspensions on hold,' as the NFL now pretends. And the Appeals Board is clearly based on the conclusion that the Commissioner overstepped his jurisdiction."
Vilma on Tuesday told ESPN's Ed Werder in a text message that he was expecting a fair hearing. Vilma walked out of a June 18 appeals hearing with Goodell, refusing to participate in what his attorney Peter Ginsberg described as a charade, and in August he requested a meeting with Goodell that he later canceled.
"I'm expecting a fair meeting, unlike the June 18 appeals hearing," Vilma said in the text. "We can all benefit from transparency regarding evidence and witnesses instead of using conjecture or hearsay to come to inaccurate conclusions. I look forward to getting this accomplished."
Ginsberg told ESPN on Tuesday that he has not been provided any assurances the league would allow the players and their legal representatives the opportunity to review evidence or cross-examine witnesses.
Those issues prompted Vilma to walk out previously.
"We want to see the evidence and confront the witnesses," Ginsberg said. "When the commissioner produces less than 1 percent of the evidence gathered in the investigation, it became abundantly clear we were not being offered a fair opportunity to present to him in a very strong and detailed manner what in fact took place and decided not to participate in what was clearly a charade."
Information from ESPN NFL Insider Ed Werder and The Associated Press was used in this report.