Since that victory earlier this month, McGregor has popped up at an event in Belfast and revealed his other half Dee Devlin is pregnant with his first child.
McGregor - now officially the sport's biggest superstar - was unwilling to set a date for his next fight after beating Alvarez, but did demand an even bigger role in a sport which has made him a global phenomenon.
In a message to UFC president White, McGregor said: "I've got a family now, so I want ownership. I want an equal share.
"Whoever owns this company needs to come to me and give me a real slice. Bring me in on this for real. Make me an owner. I need to be set for life."
McGregor, meanwhile, would consider an offer from wrestling powerhouse WWE, according to his agent Audie Attar.
UFC's main man is considering his next step but that could well come in a different sport altogether, according to Attar.
"I think it's all about business,' said Attar. "If [WWE] is going to come with an offer, we are willing to entertain it.
"We are here. Have their people call his people - which is me. We can have a conversation."