Considering McGregor is contracted exclusively to the UFC, any fight involving the Irishman would have to be run through the organisation - not something that would likely appeal to five-division boxing world champion Floyd.
"Conor McGregor is under contract with the UFC. Listen, if Floyd wants to fight Conor, call me Floyd," White said last week.
Regardless, McGregor doesn't appear to be holding back in his fight preparations, despite the fact that his name doesn't appear on any UFC cards in the near future.
After posting a number of images on his social media accounts, all signs seem to suggest that the "Notorious" is preparing himself for a fight in a square ring.
Sparring
Two days after he posted an image with former IBF welterweight international champion Chris Van Heerden to his Instagram account, footage surfaced on Wednesday of McGregor sparring at the Box'N Burn gym in Brentwood, LA.
The two minute video showed both southpaws facing off in headgear and regularly tagging each other.
McGregor understandably copped more than what he dealt out, and was accused by some viewers of lacking head movement a correct boxing stance.
According to the video's description, which was posted by the official Box'N Burn YouTube channel, the footage showed just the first of 12 rounds.
Soon after the video began circulating online, it was made private by the user, hiding it from the public eye.
"Video is private now... anyone have a mirror?" one Reddit user said.
"In less than hour, too. Would have liked to see this," another commented.
Van Heerden even gave his partner the tick of approval, writing on Twitter that McGregor was "right up there" with some of the top fighters he had sparred against.
Van Heerden is certainly no mug in the ring, with a record of 24-2-1 and almost 10 years as a professional, the 28-year-old knows a thing or two about sparring - not a bad partner for someone potentially preparing for their first boxing match.
Not everyone is convinced that McGregor's recent obsession with boxing is indicative of a looming superfight however, with the possibility of a rematch with Nate Diaz raised.
MMA pundit Tom Rooney of the Independent claimed McGregor was preparing for a rematch with the UFC welterweight after sparring with a boxer of the same weight class.
"Conor McGregor is currently in Los Angeles enjoying the sunshine while preparing for an unspecified bout, but if his latest sparing partner's physical dimensions are anything to go by, it won't be against Floyd Mayweather," Rooney said.
"The showdown between the Dubliner and Nate Diaz, which was pulled from the main event slot of UFC 200 when the former refused to fulfil media obligations, will soon be rescheduled.
"McGregor recently sparred with South African boxer Chris van Heerden who, funnily enough, has an uncannily similar frame to that of Diaz.
"The former IBF welterweight champion stands at 5'11" - just an inch shorter than the Californian - and is also a rangy southpaw."
