The Irishman publicly praised the president on Twitter, while Trump congratulated him for his win in UFC 246 on Saturday night.
Mayweather retired for a third and final time after defeating McGregor in August 2017 but his latest Instagram post suggests a comeback may be on the cards.
The Irishman is a heavy favorite to come out on top in Las Vegas in his first professional fight since October 2018.
The 25-year-old "Sorry" singer claimed he was joking about fighting the Hollywood star.
The 25-year-old singer took to Twitter to announce he wanted to take on the 56-year-old action movie star in a UFC clash.
The Irishman announced his retirement from MMA via a post on his Twitter account on Monday night.
McGregor allegedly left the famed Fontainebleau Hotel with a fan and smashed their phone when the fan tried to take his photo.
Most of the teams the rapper has pledged allegiance to seem to be jinxed.
The Irishman has been suspended from driving for six months after pleading guilty to speeding.
"You accomplished the main goal: You won the fight, with confidence and dignity," Putin told the fighter.
"Money" Mayweather improved to 50-0 with his win over the MMA champion.
By the eighth round, the most feared man in the UFC was scuffling with all the ferocity and accuracy of a middle manager arguing with a colleague at after-work cocktails.
The two celebrities are showcasing racism, oppression and hatred in all their forms.
In the space of less than a week, Conor McGregor and Floyd Mayweather have thrown mostly everything at each other except physical objects and their fists.
The two men traded insults in Los Angeles ahead of their fight on August 26.
The Filipino boxer enters the ring on Saturday, against Australian Jeff Horn.
The Irishman is known for his showmanship outside the ring.
The Canadian died on Sunday having fallen into a coma.
The pair will meet in Las Vegas on August 26.
McGregor will switch sports to take Mayweather on at boxing.
The UFC president will speak to the McGregor camp on Sunday.