might have the smoking gun he needs to get his indefinite suspension overturned -- audio of NFL exec Troy Vincent
seemingly promising the Vikings star he'd only sit for 2 games.
Peterson had previously claimed Vincent made the promise, but now -- 2 days after an arbitrator denied AP's appeal
to overturn the suspension -- ABC News played audio of the Nov. 12 convo between Vincent and Peterson.
On the tape, Vincent never uses the p-word, but does say ... "I gave you my word." He also hints Peterson needs to "go through the process" quietly. Translation: keep your mouth shut, don't blast the league ... and you'll be back on the field in no time.
The NFL Players Association filed a lawsuit Monday on AP's behalf, challenging the decision on Friday to uphold his indefinite suspension.
Earlier this month we talked to Vincent about the alleged "promise." Interestingly, he didn't say AP was wrong for calling him out -- and only said he was "praying" for him.