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Paul took former pound-for-pound king Floyd Mayweather the distance in their exhibition bout last month.
He's been linked with a contest against UFC legend Anderson Silva, but 'Iron' Mike is trying to get the 'Maverick' to fight ex-two-weight world champion boxer Badou Jack.
The 37-year-old, who owned world titles at super-middleweight and light-heavyweight, is interested in facing Paul - though isn't convinced he'll step up.
Speaking on his podcast, Tyson said: "I'm trying to get Logan Paul to fight Badou Jack. I wanna see what he says about that.
"He is stupid enough to do it. That would be so beautiful, if that could happen.
"He did really well in the Floyd fight, so it's a possibility he could go a couple of rounds with you, a couple of exciting rounds."
Jack replied: "I'll fight him. But do you think he'd want to fight me?
"I don't believe he's got the balls to fight me. I don't think he's stupid enough."
Jack actually last fought on the undercard of Mayweather vs. Paul, stopping Dervin Colina inside the distance.
'The Ripper' boast wins over Anthony Dirrell, George Groves and Nathan Cleverly, among others.
Paul vs. Jack? Watch this space.
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