The 26-year-old American star clashed with Mayweather in an eight-round bout at the Hard Rock Stadium in Miami, Florida, earlier this month.
However, Paul defied the odds by going the full distance against the 44-year-old former boxer, despite no official winner being crowned from the contest.
Mayweather dominated the YouTube star in the fight, with fans even claiming that he knocked out Paul after damning footage emerged.
Paul has since dismissed the conspiracy theories and told his critics to "shut the f**k up," as he accused viewers of "trying to spin it" and discredit his performance.
Now, ringside footage has been uploaded by YouTuber AGFILMz, which shows Paul talking to Mayweather and reminding him of the purpose of an exhibition fight.
Separated by referee Samuel Burgos, Paul could be heard saying to Mayweather: "Chill, champ, chill, it's just an exhibition."
Mayweather, who retired in 2017 after notching up his 50-0 boxing record, ruled out an immediate return to the squared circle for another exhibition fight.
"As far as me fighting again, absolutely not. As far as me doing another exhibition, probably not," he said.
Speaking after the Mayweather fight, Paul claimed a moral victory over his critics after saying that he proved the "odds can be beat."
The Maverick said: "I don't want anyone to tell me anything is impossible ever again.
"The fact that I'm in here with one of the best boxers of all times proves the odds can be beat."
UFC Legend Khabib Nurmagomedov has since claimed that the Mayweather vs Paul fight had no "competitive aspect to it."
Logan's younger brother, Jake Paul, made a bold claim that his sibling "did better than Conor McGregor" in his fight with Mayweather.
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