Only BJ Penn has attempted the feat previously and he fell short in his bid when he lost to Georges St-Pierre at UFC 94 in 2009.
Conor McGregor takes on Eddie Alvarez at UFC 205 for the lightweight title in a bid to become the first man in UFC history to hold two titles simultaneously.
"If there wasn't a contract or anything holding me back, I don't think (I would fight again)", Aldo said.
"Let me see the pictures on publications with a belt on each shoulder first", he recently told SI by phone.
".let me do it and let me go back and look at some pictures of me with two belts and let me embrace it for half-a-day", said McGregor.
"They asked me a question about respect so I answered that with an example", he told Press Association Sport. "For UFC it's very easy when you keep a lot of your staff starving, they are easier to control", St-Pierre said.
But that hasn't stopped Conor McGregor from taunting the boxing legend.
Water bottles and energy drink cans were thrown by both camps at a pre-fight media event at the MGM Grand in Las Vegas ahead of McGregor's UFC 202 victory over Nate Diaz, whose hearing is likely to take place next month. "I fought two times on the same card as Bisping and we were scheduled to fight in London (at UFC Fight Night 84). That's what everyone should be excited about, this is history".
McGregor, 28, is under contract with the UFC, and any potential fight against Mayweather (or anyone else) would have had to involve a co-promotion or the UFC's blessing.
White and McGregor seemed to be at odds regarding the relinquishing of one of the belts, but the Irishman believes the media have played their part in the debacle. The conversation was great, I thanked them for everything they did for me, and thanked Dana for his patience. "I'm not that kind of guy", Aldo said. "I came here because I had a lot on my chest, a lot I wanted to say, and I thought saying them in-person was the professional approach ..." We will have to park this conversation between Dana and the rest of the group for now, because it's a new group of people, but we can have a final decision of what is going to happen in the future. He'll have accomplished this and then he'll have to figure out which one he wants to give up.
"I work and I hustle like I'm not in the position I'm in".