The highly anticipated boxing match between the duo was confirmed earlier in June as the two combat stars will meet in Las Vegas on 26 August.
According to Sun Sport, the first press conference involving the pair will take place in London at the Wembley Stadium where a stage will be erected at one end of the pitch.
While there is no official date, the report claims it will happen in two weeks in what will be a free event with 10,000 people expected to turn up.
It will be the first of many press conferences that will take place around the world in an effort to hype the fight up even more and truly make it a global attraction.
This is not the first time that McGregor has taken part in a world tour. During the year-long buildup of his UFC 194 featherweight title fight with Jose Aldo, he travelled with the Brazilian to eight different cities across five different countries in 11 days.
Throughout his tour of Las Vegas, Los Angeles, Boston, New York, Toronto, Rio de Janeiro, Dublin and London, the Irishman verbally assaulted Aldo. Many claim that was a huge factor in the former featherweight champion's eventual 13-second loss to McGregor.
Many believe that the "Notorious" should do the same to Mayweather if he wants any chance of pulling off arguably the biggest upset in combat sport history.
Former UFC middleweight champion Chris Weidman predicted in April that the fight would be an easy win for "Money" but that his head would be spinning from all the trash talk that would come his way from McGregor.
"Obviously McGregor has no chance in that fight," Weidman said. "But everyone's still going to pay to watch it because it's Floyd Mayweather and Conor McGregor is going to talk."
"He's going to say things to Floyd Mayweather that no one has ever said to him before. He's going to have Floyd Mayweather's head spinning. It's going to be insane. It's going to be an amazing event."