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Jake is set to make his return to the boxing ring against former UFC welterweight champ Tyron Woodley in an eight-round clash on 28th August.
Logan, meanwhile, has only fought in one professional fight as he suffered a split-decision defeat to YouTube rival KSI in their 2019 blockbuster bout.
But the 26-year-old YouTuber also clashed with boxing legend Floyd Mayweather in an exhibition fight at the Hard Rock Stadium in Miami, Florida, earlier this month.
The Paul brothers have previously been linked to face each other in what would be a lucrative fight, which included Logan issuing the challenge to his younger brother in January.
Speaking to Brendan Schaub on Below the Belt, Jake revealed that his parents weren't thrilled with the idea of him facing his older brother.
The YouTuber-turned-boxer added that he wanted his "kids to drive Rolls-Royces" as Jake acknowledged the hefty payday he could receive from a fight with Logan.
Jake told Schaub: "No, no. My dad and my mom are already p****d about this. They're like, 'Absolutely not, we don't want you to do it.'
"[...] I said, 'Mom, I had a $3,000 car that I had to landscape to pay for as a 16-year-old.'
"I want my kids to drive Rolls-Royces, so let me fight my brother. But it's kind of a joke, it's kind of not.
"Our relationship just keeps on getting better and better, so it's like I don't know. I don't know."
Logan has insisted that a fight with Jake would "create a spectacle that has never been done and would probably never be done again."
The American YouTube star told CBS Sports: "Everyone asks this question. I really do believe part of the reason I was put on this earth was to entertain and to put on a show to alleviate.
"I think me fighting Jake would create a spectacle that has never been done and would probably never be done again. That excites me."
Featured Image Credit: Below the Belt with Brendan Schaub/Logan Paul's Instagram
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