Mayweather stopped McGregor in the 10th round when the UFC superstar made his professional boxing debut in August 2017.
The unbeaten Mayweather retired for the third time after that bout, but announced last November that he would resume his career yet again in 2020 for a "spectacular event".
McGregor will make his UFC comeback against Donald 'Cowboy' Cerrone on Saturday and the 31-year-old Dubliner took the opportunity to call out Mayweather prior to the fight.
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— UFC (@ufc) January 14, 2020
He told told Ariel Helwani's MMA Show on ESPN: "Most certainly, I'd like to rematch Floyd. I think we should rematch Floyd.
"He keeps flirting with it [coming out of retirement] and he can go and pick someone else but it's not going to be the same. I did phenomenal in that fight and the only reason I lost that bout was because I prepared for a back-foot style of opponent.
"And when the fight was like that I was picking him apart. Then he came forward and started pressing and I wasn't sinking into my shots like I am now with my boxing coaches.
"I know I'd beat Floyd if we rematched. When we rematch. It's not going to be a mixed martial arts bout like he said. It was supposed to be me boxing then we'll do a mixed martial arts bout.
"It wasn't written but it was verbal. But that's not going to happen and I'm not even going to push him on it."
Leonard Ellerbe, Mayweather's boss, tweeted in reply to a video of the interview: "@TheNotoriousMMA are you really sure about that champ, you know we can make that happen, asking for a friend?"
Photo Getty Images Caption: Floyd Mayweather Jr (left) and Conor McGregor (right)