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Hearn and Paul have teamed up to promote this weekend's blockbuster showdown between Katie Taylor and Amanda Serrano.
They held a media scrum to talk up the world title bout, but attention turned to the 25-year-old's budding boxing career.
The Matchroom boss was quizzed about Paul's dream of becoming a world champion to which he replied with a damning assessment.
In a clip uploaded by iFL TV, Hearn tore into Paul as he referenced Tyron Woodley and Tommy Fury.
"Everyone's entitled to have a dream, [but] I think there's absolutely no way he can beat a world champion and become world champion," he told reporters.
"But I will say he's improving a lot, he's dedicated to the sport. I don't know how good he is because he hasn't really faced a real fighter yet. It's not his fault, he signed to fight Tommy Fury..."
Not having Hearn's rant, Paul argued: "A five-time world champion in Tyron Woodley is a real fighter."
The 42-year-old Brit, however, hit back: "Mate, he's not a real boxer. He's not Jake. A real boxer is someone that that is his craft.
"What I'm saying is, [Woodley] does not qualify to give you any right to talk about fighting for a world title - and nor does Tommy Fury actually.
"But, I'll give you the props, I'll give you the respect, you're improving all the time, but the proof will be in the pudding.
"By the way, I have said that I think Jake Paul is better than some fighters. But I don't believe you will ever get close to being a world-class fighter."
Paul was supposed to face Fury before he withdrew, with 'The Problem Child' facing Woodley for a second time.
He stopped the former UFC welterweight champion to record his fifth professional victory.
Paul's expected to return to action in the summer. Will he become a world champion? Let us know what you think.
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