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The YouTuber turned combat sports star is now 5-0 in boxing after knocking out Tyron Woodley and Ben Askren last year, with a transition to MMA rumoured.
Paul said he would train with Nurmagomedov and Mendez at the AKA gym in San Jose, California but those claims have now been shot down.
Mendez told The Schmo: "It could happen but like anybody you know we have to go through all the coaches and all the fighters that are here and anybody that's a famous athlete like him.
"They will go through the routine that everybody does so he would have to get voted by everybody. First of all, he's never asked. What he's done is he's marketed himself beautifully.
"I loved the plug he gave us, I think it was a fantastic plug and I think he's a fantastic person. He in turn gave me a create return favour by talking about training with us."
Mendez helped Nurmagomedov become UFC lightweight champion before he retired in 2020 with a perfect 29-0 record.
He continued: "The reality is no matter who you are, you have to go through the team to get consent to train with us. He hasn't been given consent because he hasn't asked, it's not that he won't I just know he hasn't asked.
"If he does get denied, he won't know who denied him cause we don't say that."
Paul hasn't confirmed when his next boxing match will be, but he's been uploading MMA training footage to social media in recent days.
He tagged Bellator and PFL in the post, but not the UFC.
UFC president Dana White is currently embroiled in a bitter war of words with the 'Problem Child' over fighter pay as well as allegations he uses cocaine.
White has stressed on a number of occasions he will never work with Jake or his older brother, Logan.
That hasn't stopped Paul trying to get what he wants however - a fight with Jorge Masvidal.
Paul said earlier this month that he'd retire from boxing 'for good' if he got a shot at Gamebred inside the Octagon.
It means any potential fight with Paul will be put on the back-burner for at least a few months.
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