Williams can be heard on the recording, taken by documentary filmmaker Sean Pamphilon last season while working on a project, instructing his players to injure members of the San Francisco 49ers ahead of their playoff game in January.
San Francisco quarterback Alex Smith and running back Frank Gore are among the players Williams mentions during a speech before the Saints lost to the 49ers in the Divisional Playoffs.
"We hit (expletive) Smith right there" Williams is heard saying, according to a report on Yahoo! US that said the banned coach also pointed under his chin.
Williams also reportedly rubbed his thumb against his index and middle fingers - the money sign - and said: "I got the first one. Go get it. Go lay that (expletive) out," he said.
The report surfaced on the same day Saints head coach Sean Payton, general manager Mickey Loomis and assistant coach Joe Vitt were to meet NFL commissioner Roger Goodell to appeal their suspensions in scandal.
Payton was suspended for the 2012 season, Loomis for eight games and Vitt for six. The Saints also were fined $500,000 and ordered to forfeit second-round draft picks in 2012 and 2013.
Williams, who was named defensive coordinator for the St. Louis Rams before news of the bounty system surfaced in early March, did not appeal his ban.
"Kill the head, the body will die," Williams was heard saying in another segment of the audio. "We've to do everything in the world to make sure we kill Frank Gore's head."
Pamphilon, who had special access to the Saints last season while working on a documentary, did not believe any players were actually injured as a result of the speech.
"I was two feet behind the Saints' bench," he told Yahoo!, "And it looked like they were trying to kill each other every play. But I've watched about 15 NFL games from the sidelines, and I didn't see anything different in that game than I've seen in any other football game."