Joshua beat Wladimir Klitschko in the 11th round at a sold out Wembley Stadium at the weekend to win three of the four heavyweight titles that belonged to Fury, who relinquished all of his titles in 2015 after his license was suspended pending investigation for doping and medical issues.
The heavyweight rivals have been talking about a match-up since last week when they exchanged barbs on Twitter and Fury challenged Joshua after his victory at Wembley, saying he "can beat AJ with one arm tied behind my back".
Hearn, who is planning Joshua's schedule, said that Fury still had a lot of hurdles to clear before a fight could be arranged.
"We are desperate for that fight because AJ thinks he wins comfortably, it is a great fight and it is the biggest fight out there," Hearn told talkSPORT. "But we can only concentrate on AJ's career and guiding him."
"He [Fury] is miles away from fighting. He is in a terrible physical way at the moment. He doesn't have a licence, he needs to go back to the [British Boxing] board, and he is under investigation for [an alleged] failed [doping] test.
"There is no one that wants to see him back more than me, but it is miles away. He is not the next fight because he won't be ready in time."
Joshua, who extended his unbeaten run to 19 fights, could face Klitschko in a rematch or challenge either Deontay Wilder (WBC champion) or Joseph Parker (WBO champion) for his next match.
Photo By: Andrew Couldridge/ Reuters (Anthony Joshua poses with his team after beating Wladimir Klitschko at Wembley Stadium in London).