"I've already told you it will be on my terms & the split will be 60/40 my end, see you summer/autumn 2019," the 29-year-old said.
Hearn has previously told UK's Sky Sports that his camp were interested in making the Fury fight come to fruition, but admitted that negotiations to turn the bout into reality would be difficult.
"Everybody wants to see Tyson Fury back and I believe we'll see him back," Hearn said.
"Like I said in interviews last week, we're ready to make the fight.
"It's not a fight that's made over social media, it's a fight that's made in the boardroom.
"It's tricky to make, because it's a voluntary defence for Anthony Joshua, but yes it's a voluntary defence against a contender in Tyson Fury that is a former champion, does have a huge amount of value in the fight as well."
Hearn's focus on a potential domestic fight between Fury and Joshua could raise some concerns regarding the importance Joshua's camp are placing on his blockbuster fight against Parker in Cardiff.
Over 70,000 tickets have been purchased for the March 31 (April 1 NZT) event at Principality Stadium.
The winner of that clash will earn the right to become the holder of the IBF, WBA (Super), WBO and IBO heavyweight belts.
A potential bout against WBC heavyweight champion Deontay Wilder of the United States could be a more attractive propsition than a fight against the unbeaten Fury for the winner of the Joshua-Parker clash, such is the lure of unifying all four of boxing's major heavyweight titles, as well as the IBO belt.
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