Williams, who left the Saints after last season to join the St. Louis Rams, ran the bounty program.
It's still unclear whether the appeals will change anything, but Goodell said Monday he's open to new evidence. He noted, though, that the investigation has lasted years, in large part because the Saints didn't come clean when first asked about the bounties.
"We've met with various personnel in the Saints, and for three years they denied that this was going on," Goodell said. "It's clear it was going on, and that's one of the reasons the punishment was harsh. ... They denied it repeatedly. And eventually we were able to get a credible source that came up late last year that gave us information that indicated clearly that it was going on."
Even then, Goodell said, the Saints still denied it.
"We want to hear if there's information we're not aware of," he said. "We'll take that into consideration and we'll deal with it from there."
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.