Nevada State Athletic Commission executive director Bob Bennett confirmed to ESPN.com that McGregor submitted his application on Thursday.
The move is critical because McGregor said he has agreed to terms with the UFC for a potential boxing match against Mayweather. UFC president Dana White said on Wednesday he had already stuck a deal with McGregor on a contract for the fight.
"The McGregor side is done," White said. "I'm starting to work on the Mayweather side now."
The contest would be "straight-up boxing," White added.
Bennett told ESPN that McGregor's application was incomplete due to missing medical documents, but when those documents are submitted, the commission would consider McGregor's request.
"Conor is intimately familiar with our licensing procedures, having fought here multiple times for the UFC," Bennett said. "When he has time, and all sides have come to a contractual agreement, I'm sure he will fulfill our requirements, and we look forward to having him fight in Nevada."
Las Vegas sportsbooks already are taking thousands of dollars in bets on a Mayweather-McGregor fight even though the bout has not been finalized.
McGregor (21-3) had been ineligible to get a boxing license in Nevada as recently as March because of an outstanding fine for his involvement in a UFC media conference last year. The Nevada State Athletic Commission originally fined McGregor $75,000 for his actions, then reduced it to $25,000.
Bennett said the decision on whether to approve a boxing match between Mayweather (49-0, 26 KOs) and McGregor would be up to the Nevada State Athletic Commission chair and the commissioners, but he said he expects that it would be approved.
No tentative date has been set for a potential Mayweather-McGregor fight.
Mayweather was in London on Thursday to promote a bout involving one of his proteges, Gervonta Davis, and he did not want to discuss the possible fight against McGregor.
"This is a Liam Walsh and Gervonta Davis press conference, let's focus on these two competitors," Mayweather said, according to the Washington Post. "That's total disrespect to both of these fighters."