It could be a mismatch. It could be a circus. It might never happen. But a lot of people seem to want to see Conor McGregor fight Floyd Mayweather Jr.And the bout inched closer to reality after McGregor and the Ultimate Fighting Championship announced that they had reached an agreement on their end.

“The McGregor side is done; I’m starting to work on the Mayweather side now,” the U.F.C. president, Dana White, said in an appearance on TNT’s postgame N.B.A. coverage Wednesday night that demonstrated again how the prospective bout has crossed over into conversation even among fans with little interest in combat sports.

“I’m not saying the fight will happen,” White cautioned.

Because McGregor, 28, is under contract to the U.F.C., he cannot just cut a deal with Mayweather on his own.

“It is an honor to sign this record-breaking deal,” McGregor said in a statement to the mixed martial arts site The Mac Life. “The first and most important part of this historic contract has now officially been signed off on. Congratulations to all parties involved. We now await Al Haymon and his boxer’s signature in the coming days.” Haymon is a promoter who works with Mayweather.

McGregor had a son on May 6 and posted a photograph on Thursday of the baby, Conor Jr., with some of his mixed martial arts belts. He added the message, “Let’s go get some boxing ones now son.”

“As soon as their side communicates with our side, then the fight will happen,” Mayweather told ESPN earlier on Wednesday.

White does not seem worried that the hype over the fight will overshadow the actual mixed martial arts events his promotion hosts. “Every once in a while, there’s this kind of fight that everyone wants to see,” he said. “I embrace it.”