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Johnny Manziel of the Texas A&M University Aggies after being named the 78th winner of the Heisman Memorial Trophy Award
Brady said he hopes to be "playing for many more years" and would look forward to competing against 2012 Heisman winner Johnny Manziel when the Texas A&M quarterback turns pro. Manziel, who became the first freshman to receive the award, will be eligible for the NFL next year.
As for the risks of playing football, Brady said, "It's a physical game. It does take a toll on you physically. You have to take it into your own hands as an athlete to understand what you're getting yourself into."
Last week, the NFL agreed to pay $765 million to settle thousands of player lawsuits over head injuries.
(Read more: NFL, ex-players in $765 million concussion deal)
"All parents are concerned about their children's well-being," Brady added. "As a parent of three kids, I'm very concerned about their well-being."
But, he said, "I think football has so much to offer this country and young athletes that want to be part of a team."
Preparation for the game and staying healthy are top priorities for Brady, and he wants to share his knowledge with the general public by starting the TB12 Sports Therapy Center in Foxborough, Mass.
"It's for athletes. It's for weekend warriors. It's for any competitive athlete that wants to perform at a high level at any age," he said, adding that the center should open in the "next week or two."
—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC