Fury is even willing to put his money where his mouth is.
"If Anthony Joshua fights Joseph Parker I will bet anybody in the world £5000 cash the [that] Parker will ko him?" Fury, back in the gym and vowing to clear his name to re-enter the division, wrote on Twitter.
The Parker and Joshua camps continue to be at odds over the value of the fight, with Duco Events boss David Higgins seething over a low-ball offer from Hearn earlier in the week.
Parker entered the fray, calling out Hearn on social media, and it seems to have stirred the British camp into trying to keep negotiations alive.
Parker sarcastically "thanked" Joshua "for offering me less than half of what you paid (Charles) Martin, to unify! Do you really want to fight? Make a serious offer".
Hearn insists Joshua wants to fight Parker and it's a matter of finding some middle ground for a 2018 clash.
"I'm not sure what Parker was told, but his tweet was incorrect," Hearn told Sky Sports. "They haven't even replied to my offer, other than via tweets. We are not interested in the he said, she said.
"If they want to make the fight, then they should come off social media and pick up the phone.
"I'm encouraging them to open dialogue to see if we can find middle ground.
"We have spoken [on Wednesday] and made our positions clear. There isn't middle ground at the moment but that can change. This is a fight we want."
The camps have been in contact but it seems Higgins is still incensed at what is being put on the table by Hearn with Joshua holding the IBF and WBA belts.
"We've had clarification from Eddie (on the Charles Martin purse). It was actually a little bit more than half that Eddie offered. But still, how can Charles Martin be worth nearly double a unification against an unbeaten world champion named Joseph Parker?"
Higgins said earlier in the week he wasn't prepared to budge below a 40 per cent cut of the deal but indicated he might soften that stance slightly.
"We want a more collaborative, open book approach, rather than pay us off with a low fixed fee and we don't know what the revenues are," Higgins told Sky Sports.
"The world wants to see it, we want it, but we won't accept it for what we think is an unfair deal.
"Joseph Parker's message to Anthony Joshua is: 'I want to fight you. I think I'll win, but I want a fair portion of the pie. It's a big pie and let's share it fairly'."
Hearn continued his line that he felt a 20 per cent cut to Parker "maybe is fair".
Hearn is also in negotiations with the camp of WBC champion Deontay Wilder about a unification bout.
Joshua wants to try to unify all the belts next year. It seems he would prefer to fight Parker first in February or March with an eye to a Wilder fight at a major outdoor stadium in the UK summer.
Photo by: @JOEBOXERPARKER/TWITTER. Caption: Tyson Fury has plenty of respect for Joseph Parker and is backing the Kiwi to KO Anthony Joshua if a unification fight can be arranged.