The Youtuber-turned-boxer had been due to take on Tyson Fury’s younger brother in Madison Square Garden on August 6 but the much-anticipated encounter fell through after Fury was stopped from travelling to America.
The failure of Fury to make the fight, for what was the second time, prompted a barrage of abuse from Paul who taunted his rival for running away.
However, Paul is apparently still considering a third opportunity to embarrass the brother of heavyweight champion Tyson as it “would make sense”.
He told TMZ Sport: “I think it’d be funny to go over to the UK and knock him out in front of his whole family.”
Paul has in the meantime agreed to face heavyweight prospect Hasim Rahman Jr instead.
The 31-year-old son of ex-heavyweight champion Hasim Sr won his first 12 fights, six by KO.
But he was beaten for the first time in April when he was stopped in round five by James McKenzie Morrison (31), the son of former heavyweight champ Tommy.
Paul’s current 5-0 victory roll includes one against an online rival, an ex-NBA star and two former MMA world champions.
Paul said: “Fury fumbled the bag for the second time in a row and went into hiding, so I’m going to step up, again, and take on a new opponent on short notice.
“Nothing but respect for Hasim Rahman Jr, a professional heavyweight boxer with a 12-1 record who comes from a legendary boxing family.
"He’s bigger, he’s stronger and he’s more experienced. But guess what? I’m crazier.
"I’m raising the stakes and on August 6, I will get my respect under the bright lights of Madison Square Garden.”
Fury said he was "gutted" after Paul terminated their fight contract when he was forced to pull out of his grudge match over his visa issues.
He has insisted the bout can go ahead outside of the USA.
He argued he and his team "could never have anticipated" him being refused entry to the US but Paul blasted his efforts to get a visa - claiming Fury Junior "wasn’t interested and literally went into hiding”.
Former Love Island star Fury had released a statement saying: "I'm gutted and disappointed in regards to issues I have faced with entry to the USA.
"This situation has been left with my lawyers as being denied entry to a country is obviously a very serious issue and needs to be resolved.
"I am confident this fight will happen when the issues get resolved.
"I want to clarify that I will fight in a neutral country that both parties can enter.
"This can be any time, any place, anywhere."
Social media celebrity Paul had earlier posted: "Fury’s received a termination notice. MVP did everything it could to help him & team.
"He wasn’t interested and he literally went into hiding. Second time in a row he has pulled out.
"Second time in a row I’m going to step up and take on a new opponent on short notice. AUG 6. MSG."
The first Paul-Fury bout was scheduled for December at Madison Square Garden, but Fury pulled out before the fight because of an infection and a broken rib.
Then Fury was not allowed to board a flight at Heathrow Airport in London for a scheduled news conference at Madison Square Garden.
In a now-deleted video posted to social media, Fury said that he, along with his “team” and lawyers, had “no clue” why he was denied entry.
But Tommy’s dad John had previously admitted he and other members of Tommy’s team were banned from entering the US due to Tyson’s links to mob boss Kinahan.
The ‘Gypsy King’ had made headlines when he was refused entry into the United States as a result of the sanctions against the Kinahan Organised Crime Group.
While none of the Furys have any association with crime, the travel bans are now said to potentially jeopardise the career of both fighters.
Over 600 people, including the world heavyweight champion, are banned from entering the US at present because of their direct association with drug boss Daniel Kinahan.