Turley said Monday that he wants Brees to disclose his level of awareness of the Saints' program, and the NFL should consider punishing the 2011 Offensive Player of the Year.
"If you're going to suspend guys like Gregg Williams, then you have to suspend ... all these guys who are anteing up money," Turley told Yahoo! Sports Radio. "And then you're going to really have to take a hard look at suspending Drew Brees. Because I want to know how much he knew. He's a representative for the union and for their health and safety."
Brees is a vice president of the NFL Players Association Executive Committee and former player representative.
Turley played for the Saints from 1998 to 2003 and was selected to the Pro Bowl in 2000. Having shown signs of serious head trauma since he left the league, Turley was offended by players being rewarded for inflicting injuries.
"That's what I've been talking about all these years, as an active player and now retired," Turley said. "Why are there so many problems with guys from the NFL in their health, from physical to mental, the way guys leave the game? It's because of attitudes like this."
Rewards for on-field achievements were prevalent in Turley's playing career, he said, and he occasionally contributed. But the payments were usually given to special teams players, and never for injuring an opponent.
"For the most part, it was statistical things that would help get a guy get a few extra bucks. ... You try to give those guys a little more incentive if it was brought up," Turley said. "I'd throw a thousand (dollars) here or there as a guy making the big bucks because a lot of guys didn't."