On Wednesday, TMZ Sports provided comments from Paul, who was a high school wrestler in Ohio before rising to fame on the video app Vine.
"I want to fight a UFC fighter," he said. "… I've wrestled my whole life."
When pushed, Paul said he'd like to fight CM Punk.
His brother, fellow YouTuber Jake Paul, said his older sibling should shoot for the stars and suggested a fight with Conor McGregor.
Neither of those bouts will happen.
UFC President Dana White gave CM Punk an opportunity to make a direct jump to the promotion despite no amateur experience. The longtime professional wrestler struggled mightily in losses to Mickey Gall in September 2016 and Mike Jackson in June.
"No, it should be a wrap," White told reporters after Punk's loss to Jackson. "The guy's 39 years old. We gave him two shots, and he had a lot of heart tonight, and I think he should call it a wrap."
He added: "That's it for his UFC career."
Punk's inability to compete was likely a learning experience for White. If Paul, 23, is serious about eventually making an impact in the UFC, he'll likely need to start climbing the MMA ladder from the bottom.
He certainly isn't stepping inside the Octagon with a two-division champion like McGregor anytime soon.