Floyd Mayweather and Conor McGregor both appear to want the fight to happen
But the Irishman has obtained a boxing licence in California and is talking up the idea of a super-fight against Mayweather.
The American has admitted that a fight with McGregor could tempt the unbeaten boxer out of retirement.
Conor McGregor: 10 things you didn't know about the UFC star
Wed, November 23, 2016
Express Sport reveals some hidden facts about the UFC star
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When McGregor travels for fights, he always needs to carry a passport for his shoes as certain states restrict certain materials. His favourite pair are made from crocodile skin
But now White has revealed why the fight could not be arranged even if both parties wanted it to happen.
"It will never happen – that's not even possible," White said.
"He's under contract with us.
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Conor McGregor and Dana White have not always got on in UFC
Conor McGregor is known as a fierce puncher in the UFC
"You have a contract for a reason.
"Let me tell you what, there are a lot of contracts out there, no matter what business you are in – UFC or whatever – and it's pretty tough to get out of a contract.
"And if Conor wants to [fight Floyd Mayweather], he's got four fights left.
"He's got four fights left with the UFC.
"Fight your four fights and, you know, go out and do what you want to do."
In the early days of the rumour, it had been suggested that the pair could get into the Octagon together in an MMA-sanctioned fight.
However, boxing now appears to have been agreed as the discipline under which the two will fight.
But Mayweather's father Floyd Sr believes that not even he could coach McGregor to a victory over his son.
"I can’t make Conor McGregor turn around from being a caveman fighter, I don’t know what he is," Mayweather Sr said.
"I’ll let my son fight McGregor and I’ll take on his trainer, whoever he is.
"I’ll knock his trainer out, I don’t even know who he is and I will knock him straight cold."