The NFL announced on Friday that their own investigation had uncovered that defensive coordinator Gregg Williams ran such a rewards scheme, including informal bonuses for knocking players out of a game, during three years at the Saints from 2009.
The issue is of major concern to the NFL which is worried about player safety issues following a series of lawsuits from former players relating to concussions.
The league has yet to announce sanctions on the Saints but fines and suspensions are among the options available to NFL commissioner Roger Goodell.
Former Washington Redskins strong safety Matt Bowen said on Saturday that a similar "bounty", made up of funds generated by the players themselves, was in operation during Williams's time with the team.
The Buffalo News reported on Sunday that cash incentives for big hits were in place while Williams was the Bills' head coach from 2001 through 2003.
Former safety Coy Wire told the paper that an atmosphere of "malicious intent" was in place when he arrived at the team in 2002.
"That's real. That happened in Buffalo," Wire was quoted by the paper.
"There were rewards. There never was a point where cash was handed out in front of the team. But surely, you were going to be rewarded. When somebody made a big hit that hurt an opponent, it was commended and encouraged," he said.
The paper said that three other defensive players from that time, speaking anonymously, confirmed that a bounty system existed during Williams' time with the Bills.
Two of those players said cash bonuses were paid for "knockout shots" that sent opponents out of games, the paper said.
Williams also worked at the Tennessee Titans, and the franchise's earlier incarnation as the Houston Oilers, and they too were accused on Sunday of operating an informal cash for hits program.
"I do know in Tennessee they definitely had bounties," former Indianapolis Colts head coach Tony Dungy, now a television analyst with NBC, told the New York Times.
"We had players that went there in free agency; we had some of their players who came to us as free agents who told us. You can draw your own conclusions from that," he said.
The Times cited former Titans player Josh Evans as confirming a 'bounty' existed but he said there was no encouragement to hurt opponents.
"It was a thing where veterans and guys on defense always put up money for things that might change the game - hard hits, interceptions, sacks," Evans told the paper.
"I have never known Gregg to say, 'Try to hurt somebody.' Guys were rewarded for making a big play or a hard hit. He probably knew. I don't think he went against it.
"It's just different times now because back in the day this stuff was part of football and nobody ever went out to try to end a guy's career, because we all had families. But I would be lying if I said you didn't want to knock a guy's butt off."
In a statement on Friday, Williams, now with the St. Louis Rams, confirmed that the system had been in place at the Saints.
"It was a terrible mistake and we knew it was wrong while we were doing it. Instead of getting caught up in it, I should have stopped it," he said.
"I take full responsibility for my role".
The only NFL team where Williams has worked which has not been linked to the practice is the Jacksonville Jaguars where he spent the 2008 season.
The Redskins on Saturday declined to comment.
Bills CEO Russ Brandon denied knowledge of any such payment system while Williams was head coach. "We would not have tolerated that type of behavior," he told the News.
The Titans were not immediately available for comment and the Redskins on Saturday declined to comment.