Paul - who rose to fame through YouTube - fought one professional fight against KSI in a boxing fight before taking on Floyd Mayweather in an exhibition fight.
During a recent interview with Ariel Helwani, Paul suggested he was open to the idea of fighting in the octagon, something UFC president Dana White has since refused to rule out.
Pimblett's popularity is at high following a first-round stoppage over Kazula Vargas at UFC London and is seen as the man to replace Conor McGregor as Europe's biggest MMA fighter.
The Liverpool star recent spoke with The Schmo and revealed he would happily take on Paul.
"He knows who the boy is, doesn't he? He knows who will put bums on seats, lad," Pimblett said.
"I can't see him mentioning anyone else. I know he's a lot bigger than me like. … I don't think it really matters, to be honest. I think I'd submit him quite easily and quite quickly but you never know, anything can happen in a fight.
"If Logan Paul ever does want the fight, lad, I'm open to hearing what numbers he's coming at us with (laughs)."