Mike Tyson, 56, in 2020 made a shock comeback in an exhibition bout against fellow legend Roy Jones Jr, 54.
And it opened the door to the possibility of future spectacle fights, with the likes of Logan and Jake Paul among those interested.
After Logan, 27, took American icon Floyd Mayweather, 45, the eight-round distance in their exhibition in 2021, he backed himself to beat Tyson.
And even the sport’s only champion with a 100 per cent knockout, who fights Anthony Yarde on Saturday, ratio agrees.
Beterbiev, 38, told SunSport: “I think Logan Paul can beat Mike Tyson of today because Mike Tyson is an old guy now.
“Mike Tyson is smoking a lot today he’s not a sportsman anymore. He’s not a fighter anymore.
“Of course Mike Tyson has a big name still but he’s not the same Mike Tyson when he was great back in the days.
“In his peak he was a monster but now he’s an old guy now. Against Roy Jones Jr, they did a good show but it was just an exhibition of 4 rounds but not a real fight.
“It was just for show and not really a real boxing ‘fight’. If Mike Tyson and Logan Paul do fight, I think it still will be a show not a good fight, like I said Mike Tyson is an old guy now.
“And he can’t fight anymore like the young fighters. Even though Logan Paul is not a boxer but he’s young and he has good health and good cardio.”
Logan had two fights against YouTube rival-turned now business partner KSI, 29, drawing the first and losing the rematch.
But a knee injury has ruled him out of a boxing return for the first time since his exhibition with Mayweather.
His brother Jake, 25, meanwhile is 6-0 as a boxer, having beaten stars of the MMA world in the process.
But he boldly claimed he would rather fight Beterbiev to Dmitry Bivol, 31, who beat Canelo Alvarez, 32, last year.
Beterbiev responded: “Tell him to call me, call my promoter.
“I’m ready to fight him I think it’s an easy fight for me. Do you think it’s a tough fight for me?