But Fox Sports US reports McGregor could follow the Californian licence approval with applications for licences to box in states such as New York, Nevada and Texas - regular destinations for the biggest boxing events in the United States.
McGregor remains under contract with the UFC and will need the company's permission to fight outside its competition.
UFC president Dana White cast doubt on the possibility of the fight occurring, appearing to indicate the fight was a mismatch and shouldn't be sanctioned.
"I have no idea what Conor is doing," White told Yahoo Sports when asked his opinion of McGregor obtaining a boxing licence. "Conor's Conor. He does his thing. But he's under contract to me. Who knows with this guy? Who knows what he is up to. I just let Conor be Conor. And the other thing is, it's fun to talk about this fight and what might happen, but what commission would let that fight happen? Really, think about that."
McGregor and Mayweather have been talking up a fight for several months. The Irish superstar's striking ability - which has been far superior to anyone he's faced inside the Octagon - had some experienced judges indicating he could hold his own against the 49-0 former pound-for-pound champion.
"It comes along once in a lifetime or once every hundred years or what not," said Mark Henry, the striking coach of UFC lightweight Eddie Alvarez. "I think God has just blessed him with a swing that I'll probably never see again. Before this fight, I would highly doubt him fighting Mayweather, but I think this dude can take out Mayweather. I'm not even joking."
But Mayweather has insisted McGregor is not in his league. "I didn't know Conor McGregor was undefeated," he told TMZ recently. "I didn't know he had a reign in MMA for 20 years and was undefeated and was world champion in five different weight classes. That's something I didn't know. So I guess you guys are telling me something new if you say he's the Floyd Mayweather of the MMA.
"If you say he's the Floyd Mayweather of the MMA, I'm trying to find out have you ever made $300 million in one night? Have you ever made $100 million in one night? Have you ever made $70 million in one night. So as far as saying he's the Floyd Mayweather of MMA - it's OK to say it but it's not true."
McGregor has consistently put a $100 million pricetag on securing his involvement in a Mayweather bout.
"Right now I have Floyd running around the Showtime offices gathering my money. That's what he's doing," McGregor said back in August.
"He's running around the Showtime offices begging for those executives to come up with $100 million cash for me, to fight me. So as soon as he gets my money, we can fight."
McGregor was forced to vacate his UFC featherweight title this week as the promotion scrambled to salvage an injury-hit UFC 206 card in Toronto next weekend.
The Irishman became the sport's first two-division world champion when he beat Alvarez for the lightweight belt at UFC 205 in New York a fortnight ago.
The UFC said on Saturday that McGregor - who is not expected to fight again until the middle of next year - had relinquished the featherweight belt which has now been given to interim holder Jose Aldo.
Max Holloway and Anthony Pettis will now headline UFC 206 in a scrap for the interim featherweight belt.
In his post-fight press conference at UFC 205, McGregor indicated he would be taking six months off to support his partner during her pregnancy - and also called on UFC ownership to offer him a slice of the company.
"They've got to come talk to me now, that's all I know," he said. "Both belts, chunk of money, little family on the way - you want me to stick around and keep doing what I'm doing? Let's talk. I want ownership now. I want the equal share. I want what I deserve, what I've earned."
