Fury, 28, has massive amounts of red tape hampering his return to the ring, which subsequently has seen the former world champion drop away from fighting fitness.
A two-year gap since his last fight with Wladimir Klitschko is already a big hindrance to making the Joshua v Fury epic a reality and Hearn wants to step in to sort out a hearing stalemate with the British Boxing Board of Control and the UK Anti-Doping Agency.
"Tyson needs to get back on the horse, and show the British public he's still serious, show the British public that he is here and back in the game," Hearn told Sky Sports.
"But, that doesn't come on social media it comes from being in the gym and getting through the ropes.
"We would like to help him clear up his stuff with UKAD and start building a schedule that will lead to Anthony Joshua."
Joshua has been linked to a unification with WBC belt holder Deontay Wilder in recent weeks, although Hearn knows the Fury fight is bigger than anything else on the table right now.
"You talk about AJ versus Wilder but it's nowhere as big as AJ against Fury," he pointed out.
"That is a fight that can be built into something huge. Two completely different characters, two completely different styles, two undefeated heavyweights, two unified champions. An incredible match up."
Already back in training, Fury has promised to be ready for April 2018, which almost certainly would be a warm-up in order to shake off the rustiness.
As Wembley Stadium is the favoured venue, a Joshua fight could be on the cards for the summer of 2019, provided Fury sticks to his plan following a number of false dawns and date setbacks recently.