Joshua, 27, and Ukraine's Klitschko, 40, had agreed terms on a world heavyweight title bout.
But Klitschko is reportedly reluctant to fight without at least one of the WBA or WBO titles on the line.
Hearn said he was "crossing fingers" that Klitschko took the fight.
Both the WBA and WBO will need to sanction the bout for their respective belts to be made available, but are yet to do so.
Britain's Tyson Fury beat Klitschko last November to win the WBA, IBF and WBO titles, before being stripped of the IBF title for failing to fight the mandatory challenger.
Britain's Joshua then beat American Charles Martin to win the IBF belt in April.
Last week, Fury, 28, relinquished his WBA and WBO belts and his boxing licence was then suspended.
The WBC belt is held by American Deontay Wilder.
"We are beginning discussions with other opponents now while crossing our fingers that Klitschko takes the fight, regardless of how many belts are on the line," Hearn told Sky Sports.
Another option for Klitschko would be to fight New Zealander Joseph Parker for the WBO belt in Germany.
"In an ideal world, there would be as many belts as possible on the line, but I hope he takes up the challenge rather than a soft touch in Germany," added Hearn.
Britain's Anthony Joshua will defend his IBF heavyweight title in Manchester on 10 December whether it is against Wladimir Klitschko or another fighter, says promoter Eddie Hearn.