Sources: Appeal decision by Tuesday

Players sources say they rejected a settlement offer in the New Orleans Saints bounty case Friday because it required some acknowledgement of culpability.

Former NFL commissioner Paul Tagliabue, who was appointed to hear the appeal, is expected to reach his decision by Tuesday, according to league sources.

The players involved -- Jonathan Vilma, Will Smith, Scott Fujita and Anthony Hargrove -- are said to be reasonably satisfied with the way Tagliabue conducted the hearings and especially that they had the opportunity to cross-examine multiple key witnesses, including former Saints defensive coordinator Gregg Williams. The players view the new information as proving their innocence, sources said.

Sources say the NFL's offer was to reduce Hargrove's suspension to two games from seven, fine Smith four game checks (Smith is appealing a four-game suspension) and leave the decision on Vilma's season-long suspension up to Tagliabue, as long as Vilma dropped his defamation suit against commissioner Roger Goodell and the league.

Tagliabue debriefed Saints owner Tom Benson this past Wednesday on the status of the hearings, sources say.

Contacted Sunday, the league said it would continue to respect Tagliabue's direction to refrain from commenting on the proceedings.

ESPN senior NFL analyst Chris Mortensen and ESPN NFL Insiders Adam Schefter and Ed Werder contributed to this report.