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'Maverick' went the distance with Mayweather earlier this month and survived eight rounds at the Hard Rock Stadium.
"You kicked his ass, I was wrong, I was wrong, you kicked ass," the 54-year-old said.
"You kicked ass, there's no doubt about it, you kicked ass."
Logan, who looked shocked at the praise he was receiving, replied: "I love you Mike."
That saw 'Iron Mike' immediately fire back with: "I'm proud of you, I'm proud of you. You went eight rounds with the greatest of all time!"
Later in the conversation, Logan said: "He was quick Mike, he was fast."
Tyson replied: "He wasn't that fast, you got him with those punches. I love you man, I love you."
The conversation quickly shifted to Logan's brother Jake, who will be fighting former UFC champion Tyron Woodley on August 28.
Paul is 3-0 and Tyson is backing both brothers in their respective boxing careers.
"Tyron's gonna get knocked the f*** out, right?" he said
"Until you guys lose I've gotta stick with you."
While Tyson is keen to stick by both brothers, that would have to change should he choose to step in the ring with them.
Logan Paul: "You can't tell me I can't beat Mike Tyson.' Bro, he's old, old"- Vontay is Typing... (@ayeyovontay_) June 18, 2021
A 54 Y/O Mike Tyson training in 2021: pic.twitter.com/eCWSu8Z3kF
Speaking on the Impaulsive podcast, he said: "Someone mentioned Mike Tyson, like how funny is it? One great at a time. Or is it like you can only fight one?
"My lawyer mentioned it and he was like, 'No, Tyson will rip your head off, you don't stand a chance'.
"I'm like 'bro, I literally just went through all of this, you can't tell me I can't beat Mike Tyson'. Bro, he's old, old."
Tyson made a return to the ring last November in a draw against Roy Jones Jr.
He is said to be interested in having another fight at some point this year.