The boxer - who is the half-brother of heavyweight champion Tyson - took to Instagram to share the news that his Electronic System for Travel Authorization (ESTA) had been denied.
In the newly uploaded video - captioned 'yesterday' - he said: "Me and my team this morning arrived at Heathrow Airport, ready for the press conference, ready to fly out, and as soon as I entered the airport I got pulled to one side and I was told by a Homeland Security officer that was there that my ESTA had been denied and that I wasn't able to travel to the USA for a reason that I apparently know.
"I can stand here and say I've done absolutely nothing wrong, I've no clue why I'm not allowed to travel to the USA.
"Like I say, I've been training for a fight this whole time and that's all I've been doing - I have no clue why they will not allow me to travel today, and neither does any of my team, or my lawyers."
He continued: "So now I'm having to go to the embassies and all this sort of stuff trying to resolve it, and I'm in the middle of training guys. I don't know why this has happened today, it's a massive shock to me and my whole team.
"Obviously it is a matter that needs to be resolved, it's government issues, it's a lot bigger than the fight right now and I'm just trying to get it sorted."
The 23-year-old is due to fight YouTuber-turned-boxer Paul in Madison Square Garden in August; at the time of writing, Paul hasn't commented on Fury's update - but we all know it's just a matter of time.
Fury told LADbible last September that he'd 'definitely' knock out Paul.
He said: "It will definitely be a stoppage win for me. A lot of people were saying after my last fight that I should have stopped that guy, but - don't forget - that was a four-round fight.
"If that had been a six-round or an eight-round fight, that guy would have been out of there.
"If me and [Jake] Paul do fight, it's going to be an eight-rounder, or even a 10-rounder, whatever he wants to do.
"I know for a fact, he can't do the eight very well. He spent at least three of the rounds, possibly four of the rounds, walking around the ring not throwing a punch, Tyron Woodley the same.
"The two of them probably threw 500 punches in the entire fight. They weren't very active.
"I would be forceful in that fight, putting him on the back foot, purely and simply because he's not been doing it for long enough."
Featured Image Credit: Instagram/@tommyfury/@jakepaul