Fury, 34, and Joshua, 32, had been in negotiations for a long-awaited Battle of Britain at the Principality Stadium in Cardiff on December 3.
But the Gypsy King took to social media to declare that the fight is officially off after his fellow Brit missed the deadline of 5pm on Monday to sign the contract.
However, Whyte thinks he needs to calm down before he does anything rash.
Boxing News – Dillian Whyte says Tyson Fury needs to ‘chill out’ as Anthony Joshua negotiations continue
Speaking to Sky Sports, he said: “He (Fury) definitely needs to chill out.
“Some of the ways he does negotiating business, it’s all social media and shouting, screaming and calling people big dossers. I’m not an Anthony Joshua fan as well, I don’t really like both of them.
“Big fights sometimes it pays off to be a bit patient, and just shut his big mouth up a bit and stop talking s**t about the big GK (Gypsy King).
“Let the fight happen, you want the fight to happen or you don’t want the fight to happen. If you want the fight to happen be patient, there’s a lot of money, a lot of things at stake so it will take time.
“It’s a lot of things that can go wrong. He just needs to relax.”
On the chances of it actually happening or not, Whyte added”I think it could happen but Tyson Fury is putting a lot of pressure on, not intelligently, he’s just trying to use social media and it’s been a bit silly really.
“These big fights take time because there’s a lot that goes into it, there are a lot of commercial things and protecting your rights. It’s not just as simple as ‘ah sign the contract you big dosser’.
“Big fights take time and they have to get everything right otherwise it will fall over at the wayside if not done properly.
“Joshua fight was simple, we’d fought already before and it was a big fight and I’ve got a good team around me so we were quick with the paperwork.
“There was no ‘the deadline is this’, we took time to protect our own interests because the fight started as a normal fight that became a pay-per-view fight a week before the fight was due to happen.”
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