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YouTube star Paul and boxer Fury, the younger half-brother of heavyweight champion Tyson, had been due to meet at Madison Square Garden on 7 August (AEST).
However, light-heavyweight Fury was denied entry to the United States in June to attend a news conference promoting the fight and the bout had been in doubt ever since.
Fury was unable to meet Paul's Wednesday deadline to resolve his visa issues, but the American intends to find a new opponent.
It is the second time the proposed fight has fallen through after Fury (8-0) withdrew last December due to illness and injury.
"Fury's received a termination notice," Paul posted on his Twitter page on Wednesday. "MVP did everything it could 2 help him & team.
Fury’s received a termination notice. MVP did everything it could 2 help him & team. He wasn’t interested & he literally went into hiding.— Jake Paul (@jakepaul) July 6, 2022
2nd time in a row he has pulled out.
2nd time in a row I’m going to step up & take on a new opponent on short notice. AUG 6. MSG.
"He wasn't interested & he literally went into hiding. 2nd time in a row he has pulled out.
"2nd time in a row I'm going to step up & take on a new opponent on short notice. AUG 6. MSG."
In response to Paul's message, Fury took to Instagram to say: "I'm gutted and disappointed in regards to the issues I have faced with entry into the USA.
"This is something that myself or my team could never have anticipated happening.
"This situation has been left with my lawyers as being denied entry into a country is obviously a very serious issue and it needs to be subsequently resolved.
"I am confident this fight will happen when this issue gets resolved and we come to a solution.
"I want to clarify that I will fight in a neutral country that both parties can enter. This can be any time, any place, any where."
Hasim Rahman Jr is one rumoured opponent for Paul (5-0), whose brother and fellow social media sensation Logan last week signed a deal with WWE.
Former Tampa Bay Buccaneers running back Le'Veon Bell also appeared to throw his hat in the ring to face Paul further down the line.
Quote tweeting Paul's earlier message, Bell said: "Please pick carefully like you've been doing cuz I don't want someone to get you outta there before I get the chance to do it."