Fury's promoter Bob Arum has questioned why a deal for the blockbuster fight is yet to be confirmed but Hearn has reiterated that there is no chance of the deal falling through.
He told Sky Sports: "This is a massive deal. No disrespect to Bob, he's an incredible promoter, he hasn't been involved in a site deal of this magnitude before.
"It takes time. When you're talking about the biggest fight in world boxing, then just a little bit of support would be nice.
"I saw that there's a new deadline. There's no new deadline. The deal is done, the fighters have agreed to the site, the numbers, they've signed the contract already.
"We just have to nail the site agreement, which is again agreed, but we have to go through the process.
"The deadline is last weekend or something, but you don't let a deal fall through because it's taking a few more days than anticipated."
Hearn also warned Arum that Joshua against Fury is the only fight that boxing fans want to see.
He said: "Bob Arum said, 'Maybe if this falls through, we go and fight Deontay Wilder.' Who wants to see that fight?"
"Even AJ against someone else? People aren't interested in that right now. The only fight that's acceptable to people is AJ against Fury, so let's make that fight happen."