The two British rivals have yet to meet for the heavyweight crown – but faced each other in a training session in 2010.
It has been claimed that Anthony Joshua “boxed Tyson Fury’s head off” when the pair met in a behind-closed-doors sparring session more than a decade ago.
At the time, AJ had only been boxing for two years but had just won the prestigious ABA title at super-heavyweight.
Fury meanwhile, was a promising and unbeaten heavyweight prospect looking for some sparring.
No one could have foreseen the impact that three-round sparring session would have had almost 11 years ago.
The pair give very different accounts of what happened, but one man with insight from ringside is Finchley trainer Sean Murphy.
And in an interview with BBC released on the latest Costello & Bunce podcast, Murphy gave his recount of the session.
He said: "I think he was expecting, because he knew he was only like 18 and hadn't been boxing long, he was expecting to have some easy few rounds.
"They've come out and Josh has thrown a jab, right uppercut, left hook and he's on wobbly legs, rubber legs!
"He's grabbed hold of the ropes and I've said to him, 'Mate, you can't hold the ropes, you've got to let go of the ropes'.
"So, he let go of the ropes and said, 'OK'. So anyway, they've done the first round, Josh really got the better of him in the first round.
"Come out for the second round I've said to Josh, 'Just go and do what you've done, relax, straight punching, nothing overly brilliant'.
"He's come out for the second round and Tyson starts mouthing off to Josh now, he's getting in his ear talking to him.
"And Josh is getting a bit wild, he's trying to knock him out now Josh and he's come back and I've said, 'What are you doing?'
"I said, 'Just stick to your boxing, do what I told you'. So he's gone out the next round, ignore the talking and just boxed his heads off."
With Fury said to have been bettered, the future two-time champion pleaded but was denied a fourth round.
Murphy said: "Tyson gone, 'No, no, no,' and he's begging for one more round.
"I went, 'Nah, get out Josh, you've done three rounds', because I knew what the craic was, he was going to try and put it on him next.
"Which Josh probably could have handled, but I wasn't going to have it because if he weighed us in we would have done five rounds, if he paid for it.
"Because, he's an an amateur boxer, I'm not letting him go in with a professional and get nothing for it."
At the time, the story goes Fury was offering any and all sparring partners his Rolex if he was dropped.
And Joshua had a sense of satisfaction knowing the expensive watch was almost his.
"I said, 'Just stick to your boxing, do what I told you'. So he's gone out the next round, ignored the talking and just boxed his heads off."
Anthony Joshua Ex-Coach On 2010 Tyson Fury Sparring Session
Murphy recalled: "Josh looked over to him and said, 'Was your Rolex up for grabs tonight?'
"And he started laughing Tyson, and Josh went, 'I nearly got it, I nearly got it'."
In an interview right after the spar, Fury, 33, said Joshua, 31, 'gave me a beating' for three rounds but years later retracted that statement.
The talking and disputing was set to be settled this summer after the two agreed terms for an all-British unification.
But Fury's attempt to walk away from his contracted trilogy bout with Deontay Wilder, 35, was denied.
Joshua and Fury’s long-awaited heavyweight world title clash has yet to come to fruition, despite Fury announcing that a date and location had been agreed for the unification bout earlier this year.
It leaves them due to rematch again on October 9, while Joshua faces mandatory challenger Oleksnadr Usyk, 34, on September 25.