The YouTuber defeated former NBA star Nate Robinson in November to record his second professional boxing win and believes that his social media popularity could allow him to take on the UFC star.
Jake said: "I think Conor and I will happen for sure.
"People will laugh at that, but what another fighter is calling him out with this big of a platform? What other fighter is calling out McGregor like this?"
Paul admits that a fight between McGregor is unlikely to happen just yet as he finds his feet in the world of combat sports but he is keen to face off against other MMA names such as Ben Askren and Dillon Danis.
He said: "Realistically, it’s not going to happen for a couple of fights. I’m cool with that. I want to knock out everyone in his camp first. Dillon Danis is in his corner, he’s the guy who got punched by Khabib [Nurmagomedov] — that’s what he’s known for — so I’ll take out Dillon Danis first. I want to bring MMA fighters into the boxing ring. That’s my goal."
Jake's brother Logan is set to fight boxing legend Floyd Mayweather in an exhibition fight next month but he is not confident of his sibling's chances.
He said: "My brother's f*****.
"It's bad for the sport. I think it's just for clout.
"I wish him the best of luck.
"I just like - don't get in there with a guy whos' never even been knocked out. He's been knocked down once and it was by accident."