The undefeated former champion (51-0) received a challenge from the Russian fighter, who was filmed by the CEO of Mayweather promotions in Leonard Ellerbe at an event in Russia saying the following.
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Mayweather, who has not fought since the McGregor bout, has said he will come out of retirement to fight Manny Pacquiao in a rematch later this year.
"Floyd Mayweather couldn't knock out McGregor but I did it quite easily".
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In an Instagram post on October 14, Nurmagomedov wrote: "Hey, let's go, Floyd".
"50 and 0 verses 27 and 0, two guys that never lose".
"CBS, Showtime and MGM Grand, get the chequebook out", Mayweather posted on Twitter.
As much as Mayweather might want to make another huge payday against a mixed martial artist, it's tough to believe he'd rake in anywhere near the kind of cash against Nurmagomedov that he did going against McGregor. White previously said that Nurmagomedov could be stripped of the 155-pound belt, though that appears to be a most unlikely scenario.
Mayweather took to social media to respond to the challenge. The graffiti also includes a speech balloon reading, "Don't talk too much" - an apparent reference to McGregor's verbal attacks on Nurmagomedov, insulting his father, religion and homeland Dagestan.
While it's unclear just how serious Nurmagomedov was in the Instagram video, his name is now red-hot for both good and bad reasons. In 2006, trainer Roger Mayweather and Zab Judah were both suspended for one year after a low blow from Judah on Floyd Mayweather in their welterweight title bout started a mid-fight fracas between both corners.