The pair’s fellow British heavyweight Derek Chisora has been beaten by Fury and sparred with Joshua, and the 38-year-old has backed “AJ” to come out on top if he faces the “Gypsy King”.
Fury has taken exception to Chisora’s claim, however, insisting he would stop Joshua within three rounds.
“This is a message for Derek Chisora,” he said in a Twitter video. “I’ve just seen that you’ve said you think AJ would blast me out.
“Never in a million years. If the biggest puncher in history [Deontay Wilder] couldn’t blast me out, and Wladimir Klitschko couldn’t blast me out, a big, old bodybuilder can’t blast me out, my friend.
“So, Del, he ain’t got the bottle to fight [Oleksandr] Usyk again. Usyk will smash him next time properly, never mind beat him on points – he’ll knock him out.
“But listen, it only takes one man like me. There’s only ever been one man on these shores, and he’s called the ‘Gypsy King’ AKA Tyson Fury.”
Fury had also attached text to the video, reading: “I’ll KO AJ in 2/3 rounds.”
Joshua was outpointed by Usyk in his last bout, in September, losing the WBA, WBO, IBF and IBO heavyweight titles in the process.
The Briton is set to rematch the undefeated Ukrainian in London in April under a new trainer, while Fury looks set to face compatriot Dillian Whyte.
Last time out, Fury knocked out Wilder for the second fight in a row to round out the rivals’ trilogy and retain the WBC heavyweight title, for which Whyte is mandatory challenger.
Fury has been ordered to fight Whyte next, though negotiations for that bout look set to head to a purse bid.