Fury posted a video on social media claiming that he would beat Joshua inside eight rounds without losing any weight, despite weighing 25 stone.
The former WBA, IBF, WBO and IBO champion vacated his belts after citing problems with depression and cocaine use.
But if he was to return to the ring, Hearn wants to see him in the gym and not just talking through social media.
“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 said.
“But, that doesn’t come on social media it comes from being in the gym and getting through the ropes.”
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Fury has not fought since beating Wladimir Klitschko in November 2015 and is awaiting a ruling from UK Anti-Doping into a suspended drugs ban.
And Hearn wants to help the 29-year-old clear up his ban to ensure he boxes Joshua.
“We would like to help him clear up his stuff with UKAD and start building a schedule that will lead to Anthony Joshua,” Hearn said.
“AJ has told me 100 percent that he has no problem with the Fury fight.
“He wants to give the public the biggest fights out there and nothing comes bigger than Joshua v Fury.”