McGregor has agreed to a boxing match and not a martial arts fight which heavily favors Mayweather.
White told American television cable channel TNT on Wednesday night that McGregor has agreed to a boxing match and not a martial arts fight which heavily favors Mayweather, who has never lost in his two-decades long storied career.
White said they still have a long way to go. But his plan now is to try to lure Mayweather out retirement for a superfight with McGregor.
"The McGregor side is done," Ultimate Fighting Champion president White said. "I'm not saying the fight will happen but I got one side done and it's time to work on the other (Mayweather).
"If we can come to a deal with (Al) Haymon and (Floyd) Mayweather, the fight's going to happen."
White said that McGregor has agreed to step in the ring with the undefeated Mayweather despite not having fought competitively in a boxing ring since he was a teenager. McGregor was granted a license to box in California several months ago.
McGregor, a 28-year-old Irishman, has been the UFC's most popular fighter and among its top money spinners while Mayweather, a 40-year-old American, retired in 2015 with a 49-0 record including 26 victories by knockout.
White has said the fight could generate a payday of $100 million for Mayweather and $75 million for McGregor. Mayweather has repeatedly said that he won't come out of retirement, against anyone, for less than $100 million.
Not everyone would be excited to see a Mayweather-McGregor boxing match.
Promoter Oscar De La Hoya has said a bout between the two would be an "embarrassment" for the sport of boxing.