The pair have been trading barbs for some time now, with Fury telling LADbible that he would comfortably beat the YouTuber.
But Paul has now taken to Instagram to make him a last offer, claiming Fury had already turned down two offers.
Paul, 24, said: "Fury has now denied two offers to fight me.
"This would be the highest pay day of his career, the best thing he could possibly do. If he really believes he can beat Jake Paul, then why would you not take this?
"Tommy, this is your last offer: eight rounds, $1 million. Eight rounds, $1 million.
"That's four times mores than you've ever been paid, so either sign the dotted line, or just stop f*****g wasting my team and I's time."
Well, Fury has now responded to Paul on his Instagram, claiming it is in fact Paul who is the time-waster.
The 22-year-old said: "I just wanted to come on here and address a few things that Jake Paul has been saying that I have denied two offers to fight him
"That is true, as those offers weren't even worth addressing, and now he has come out and said that he wants to give me a $1 million to fight him and I just want to say this.
"To everybody out there, $1 million for a fight of this magnitude is not even worth getting out of bed for, this fight is going to gross millions and millions of pounds.
"I cannot walk down the street without anybody asking me when are you fighting Jake Paul, so until you want to make a serious offer and put it on the table, we can't think about fighting pal."
He continued: "This is a very smart tactic in what he is doing. It is used by a lot of fighters when they don't want to fight somebody.
"It makes it out to the public that he has made plenty of offers, reached out to have the fight and I have turned it down and I don't want the fight.
"But as I previously said, in boxing terms $1 million is nothing especially for a fight of this size, tomorrow or tonight is soon enough to fight you get your figures up and we can talk."
Featured Image Credit: Instagram/Tommy Fury/Jake Paul