Sean Payton has met with the league commissioner in an attempt to reduce his indefinite suspension for his part in the scandal that saw players receive thousands of dollars in payoffs for delivering hits that forced opposing players out of games.
New Orleans Saints coach appeals NFL 'bounty' ban
Goodell heard appeals from various Saints representatives for six hours on Thursday and could render decisions as early as Friday, NFL.com reported, although it is more likely the rulings will come next week.
Former Saints defensive coordinator Gregg Williams, the instigator of the pay-for-injury programme that ran from 2009 through 2011, was subsequently hired as defensive coordinator for the St. Louis Rams.
He was suspended indefinitely and has not appealed his punishment.
Williams has confessed to running the bounty scheme and apologised for what he called a "terrible mistake".
However, Goodell also suspended head coach Payton for all of the 2012 season for his role. The Saints organization was fined $500,000 and docked two second-round draft picks.
An NFL probe uncovered the bounty programme, finding between 22 and 27 Saints players took thousands of dollars in payoffs for delivering hits that forced opposing players out of games.
The NFL said that in addition to known bounty targets Brett Favre and Kurt Warner, the Saints had targeted at least two other opposing quarterbacks, Cam Newton of Carolina and Aaron Rodgers of Green Bay.
Beyond punishing Saints coaches and executives, the league must still decide if players involved in the bounty programme will be disciplined.
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