"No, I met him a couple of times," Brady said. "I think he's a great fighter. That was a great fight the other night."
Mayweather had told ESPN's Sal Paolantonio last week that he and Brady were friends.
"That's a close friend of mine. Tom Brady is a very, very close friend," Mayweather said. "An unbelievable guy with unbelievable talent...he's a great guy. Actually, Tom Brady texted me yesterday.
"We have a cool friendship. He texted me and asked me 'How's everything going?' And I texted him back: 'Everything is cool, how you doing? How's the family?' And he said, 'Everything is going A-OK.'"
Brady reiterated the two had only met a "couple times" when pressed further. He did, however, compliment Mayweather as a "great fighter" and said he watched the boxer's 10th-round TKO of Conor McGregor on Sunday—a day after attending a friend's wedding.
This is the second time this year Brady's alleged friendship with a controversial figure has made headlines. President Donald Trump has counted Brady as a friend for years, and the Patriots star even had a Making America Great Again hat in his locker in 2015.
Trump has become one of the most controversial presidents in United States history in his brief seven months in office, due in large part to his handling of societal issues. Brady has maintained he does not agree with all of Trump's political viewpoints.
Mayweather has been convicted of domestic violence on multiple occasions and spent two months in jail as part of a plea deal in 2012.