Fury, who is the 23-year-old half-brother of world heavyweight champions Tyson Fury, was denied entry to the United States last month for a scheduled press conference.
Paul gave his opponent additional time to resolve his visa issues, but has now revealed that a termination notice has been received by Fury's team.
In a post on social media, the 25-year-old American said: "Fury's received a termination notice. Second time in a row he has pulled out.
"MVP [Most Valuable Promotions] did everything it could to help him and team. He wasn't interested and he literally went into hiding.
"Second time in a row I'm going to step up and take on a new opponent on short notice."
The pair were initially scheduled to box last December, however Fury pulled out of the bout citing a chest infection and broken rib.
Paul is now understood to be eyeing a short-term replacement for the fight at Madison Square Garden on August 6.
One man who could take Fury's place is Hasim Rahman Jr - the son of a two-time world heavyweight champion.
Rahman Jr and Paul are no strangers, considering the pair sparred together two year ago ahead of the YouTuber's pro debut.
The heavyweight boxer has a record of 12-1 with six knockouts to his name. His latest outing did end in a defeat as he was stopped by James McKenzie Morrison in April.
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