Fury, 34, recently offered to fight the former World Champion in a long-awaited clash in the UK - but efforts to make the fight have been paused due to the recent passing of Queen Elizabeth.
Frank Warren, Fury's promoter, told 'TalkSPORT Fight Night': "We’ve put it all on hold at the moment. It wasn’t appropriate obviously. That’s how we feel."
Despite this, Fury remains committed to making the fight, and Warren confirmed that talks over the event will soon recommence.
He shared: "We’ve put it on hold and will pick up on it in the next week or so."
Fury - who is the WBC champion and undefeated as a professional - recently offered Joshua a 40 percent split of the money for their proposed fight.
The outspoken star also urged his long-time rival to sign the contract and fight him in front of the British fans.
Fury - who has proposed fighting at either Wembley Stadium or in Cardiff - said: "I think it split is more than generous.
"I didn’t want to go in and start offering them 20 percent like they would’ve done to me.
"However, I really want this fight to happen as Oleksandr Usyk – the little middleweight – doesn’t want no smoke like I thought he didn’t and now I’m going after AJ.
"I’ve already beat Deontay Wilder so there’s only one other person and that’s AJ – the bodybuilder! So, why not give him 40 percent? Give him no excuses and let’s get the fight made for the British public."