Mayweather is generally considered to be the finest boxer on the planet, having maintained a 45-fight unbeaten record throughout his 18-year professional career.
However, Bradley, who will square off against Manny Pacquiao on April 12, told Fighthype: "Floyd Mayweather is the best pound-for-pound fighter in the game.
"I have not yet accomplished what Mayweather has been able to do, so by no means can I say I'm the best pound-for-pound fighter in the game even though I could have a win over Juan Manuel Marquez and Manny Pacquiao.
"The only way that I can say that I'm the best in the world is fighting Mayweather and beating him."
Another potential opponent for Mayweather is Amir Khan, with the two fighters' teams said to be in discussions over a May 3 dust-up in Las Vegas.