"I won't talk about the deal but what I will say is that a rematch isn't for [Joshua's] protection, it's a carrot to show [Parker] what's possible - it's an incentive to get him to take the fight," Hearn said from London.
"If he wins, he's going to make an absolute fortune in the rematch. If it's a good fight and Joe loses, we'll do it again no problems. If he beats AJ, the first fight he will want after is a rematch because it's the biggest fight in boxing. If he does win he's also going to be the biggest star in the sport."
Hearn said he hopes to have the deal signed in days. Higgins is likely to fly to London in the next few days.
Parker will likely join Higgins in London for a press conference alongside Hearn and Joshua in the second week of January which has the potential to be a fiery affair.
The near constant belittlement of Joshua's chin, described as "glass" by Higgins, has rattled Joshua and the big Englishman is said to be furious.
Hearn admitted: "They've got under his skin. The press conference is going to be a lot of fun."
He added of Higgins: "He talks a lot but he's a character and the sport needs those. There's a method in his madness."
And while riches, glory and three heavyweight world title belts were up for grabs, both men were risking it all.
Hearn said Joshua was keen to maintain his record of having won every professional fight within the distance.
Hearn was relaxed about neutral officials - one of Higgins' preferences - but said he wouldn't be surprised if the British Boxing Board of Control went for a panel comprising a Brit, a New Zealander and a neutral.
"I don't have a problem either way because I don't think this fight is going 12 rounds. But I accept we have to do what is right by our fighters."
Hearn said the bout, a "legacy" fight, had all the makings of a classic and could bring the best out of both men.
"Both are aggressive fighters. AJ likes people to come on to him. He's much better technically than people make out. Joseph will step up and look better than he did in his last fight because no one is going to look good against Hughie Fury - he didn't come to fight."