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Nunes is the women's bantamweight and featherweight champion and arguably the greatest ever female fighter in UFC history.
The Brazilian expressed her interest by simply replying "I'm in!" on Twitter.
But the YouTuber-turned-boxer is not keen on any intergender bout with the Lioness and is instead desperate for a boxing contest with McGregor's teammate Dillon Danis - where he believes there's much more bad blood.
"Nah, I wouldn't fight her," Paul told TMZ Sports.
"Waste of time. No one knows who she is.
"There's not a lot of hype there. Plus, there's no history.
"I wanna knock out Dilon because we've been talkin' s**t back and forth for 2 years, I've hooked up with his girlfriend, he's all butt-hurt about it, there's history there.
"So, why would I waste my time doing some bulls**t like [boxing Nunes?]."
Paul, who is 2-0 in professional boxing and knocked out former NBA player Nate Robinson last month, has been calling out every fighter under the sun.
But he's especially desperate to fight Danis. Having recently hurled water balloons at him in a drive-by attack that many felt was staged, he's shared a screenshot of a $500,000 offer he sent to Danis.
In the Instagram message, Paul stresses he wants to "cut out the middleman" and make the fight happen.
The 24-year-old also said there was the potential for the sum to increase to $1 million - with Paul revealing he would be willing to lose some of his purse to get it done.
Ben Askren and Michael Bisping have both said they have no problem with fighting him in the ring, while Paul posted a video mocking everyone he's been beefing with of late in an attempt to try and further rile them up.
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