The New Orleans Saints quarterback, however, did say that he probably wouldn't even tell his own wife, Brittany, if he was dinged or got his bell rung in a game.
"I wouldn't want her to worry," Brees told "The Dan Patrick Show."
Brees agreed that the idea of self-reporting concussions is a "gray area," because players don't always know when they suffered a concussion and because they might be too competitive to take themselves out of a game.
Brees shared a story he has often told in the past about how he didn't take himself out of a game after suffering the only documented concussion of his career while with the San Diego Chargers in 2004.
"I knew that something was not right. I knew that I was concussed," Brees said. "But I didn't take myself out of the game. I mean, I stayed in the game and played as long as I could until finally a coach pulled me aside and was like, 'I'm looking out for you here, and you're not gonna play anymore.' ...
"And that's why it's hard to change that mentality for guys. When you're in the heat of the moment, heat of the battle and it's competitive, you do not want to pull yourself out. That's why the concussion protocols are in place where you've got the independent neurological consultants and the trainers and the referees. Everybody's supposed to be looking."
Brees made several media appearances Thursday as part of a different type of health campaign -- "The Heat Factor" -- to promote awareness of the signs and symptoms of exertional heat stroke, particularly in high school and younger players.
Among other topics Brees discussed:
• He told Patrick that he doesn't agree with the rule change to 10-minute overtimes, "because more games are going to end in ties now." Brees said he wouldn't be opposed to using the college overtime rule.
When asked what one thing he would change in the NFL, Brees went back to the issue of commissioner discipline, which has been a popular topic for him since his days as a NFL Players Association leader and his strong belief that the Saints and Sean Payton were wronged in the league's Bountygate investigation.
"I don't think anyone would trust a league-led investigation [now]," Brees said, citing "no credibility" and "no transparency."
• Brees told the NFL Network's "Good Morning Football" that new Saints running back Adrian Peterson "obviously brings another dimension to anybody's backfield." But he stressed that Mark Ingram is "one of the best running backs in the league, certainly all purpose, from what he does just on first and second down to third down and pass protection to the passing game."
• Brees told ESPN's NFL Live that he thinks it's a "natural transition" for quarterbacks like Tony Romo and Jay Cutler to go to the broadcast booth because of the "level of knowledge about the game" required at that position. However, Brees added, "I could see them both on the field again."
Brees, 38, reiterated he "absolutely" thinks he could play until he is 45, if that's what he wants to do. However, he's still "in the heat of now" to think about when his career will end.