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The pair were set to clash in the ring on August 6 as part of a card that also featured Amanda Serrano, but Paul has now cancelled the bout after Rahman failed to meet the agreed weight of 200 pounds.
Paul's Most Valuable Promotions released a statement claiming Rahman had agreed to fight at 200lb, only for his team to later look to increase the weight limit to 215lb.
"Hasim Rahman Jr. has pulled out of the fight. This is not a joke, I am devastated, I can not f****** believe this. We just found out this news," Paul posted on Twitter.
Yet again my opponents has pulled out of the fight… (1/2) pic.twitter.com/7ADOku3glx— Jake Paul (@jakepaul) July 31, 2022
"This is just another case of a professional boxer, like Tommy Fury, being scared to fight me.
"It's clear as day that these guys have been so unprofessional to work with, looking for any excuse to suck more money out of this event, to coerce us into doing things.
"From the jump, I knew from the bottom of my heart that this guy didn't want to get into the ring with me. It's clear as day."
Rahman initially stepped up to face Paul as a replacement for Tommy Fury, who pulled out of a scheduled fight against Paul last year due to injury and then could not travel to the United States due to a visa issue.
While Rahman confirmed he was not able to meet the agreed weight, he disputed Paul's claims about money and said he would have fought for $5,000.
"I signed a contract to make 200 pounds within the three and a half weeks I had to do it, but I couldn't do it. My body simply would not let me do it, would not let me get down to 200 pounds," he said in a video message.
"But when in boxing do you see them cancelling fights a whole week in advance? I didn't even get my last week to get down as low as I could.
"I told this man: 'If there’s penalties involved, keep the purse. I'll fight you for the $5,000 minimum.'
"That's how much it means to me and that’s how much faith I have in knocking him out."
Paul would have received a WBC ranking for the first time had he defeated Rahman.