Brit Joshua defended his world titles against Carlos Takam in Cardiff a fortnight ago and has now set his sights on unifying the heavyweight division.
WBC title holder Deontay Wilder appears top of the list with WBO champ Joseph Parker also an option according to promoter Eddie Hearn with Fury out of action after being suspended from boxing after testing positive for a prohibited substance last year.
But that didn't stop Joshua putting Fury in his sights on social media during a string of tweets with Fury now responding with a taunt of his own.
"This is a message to the weight-lifter, big Anthony Joshua - the tough man. Who told me to get fit?" he said on Instagram. "To be honest with you, I don't need to get fit to fight somebody like you, at all.
"I'll come to you and I'll punch your face in for you. Even at 25 stone. So I really don't need to get fit for you, put it that way."
Joshua was made to work for his 10th-round stoppage Takam and Fury believes he's got the 28-year-old figured out.
"I've seen what you're about," he added. "Useless - no gas, no stamina, too many weights. You want to practise on a bit more speed and less power."