"My dream is to play a game here in China someday," Brady said. "We had an opportunity, I think, 10 years ago, and my team was going to play here, and unfortunately it didn't work out. But one day I hope that there are many games here, and over the course of a year, because it's such a great sport and because I love it so much, to bring that here and to bring the discipline and incredible strategy involved."
The Patriots were slated to face the Seattle Seahawks in a 2007 preseason game, but the contest was canceled as the NFL chose to focus on the debut of regular-season games in London, which began later that season.
Brady, whose trip was part of a promotional tour for Under Armour, posted a photo on Instagram of him throwing a football on the Great Wall.
He also took part in a martial arts demonstration.
Brady is headed to Shanghai on Tuesday and will visit Tokyo on Wednesday. Before the trip, he said he was eager to travel to Asia.
"I am excited about the opportunity to be able to connect with the people in China and Japan, experience the incredible culture and share my love for the game with my fans," Brady said. "The tour will be rewarding for me as I experience Shanghai, Beijing and Tokyo. I hope to learn more about the next generation of athletes in Asia and to inspire them to always push boundaries through hard work, dedication, humility and perseverance both on and off the field."
The Associated Press contributed to this report.