Hearn told IFL TV: “We’ve said to Eubank that is the date. And if you don’t take the fight on that date, the fight doesn’t work.
“There are no stadiums available. Commercially you guys are on a fortune. So if Eubank is not prepared to take the fight on September 20, I don’t think there will be a fight. That’s not my decision, that’s a decision of [Alalshikh].
“Eubank probably can’t be bothered to go back into camp. I’m not sure if he’ll ever fight again.
“I just got the feeling he just don’t want it.”
The April fight took place 35 years after their legendary fathers – Chris Eubank Sr and Nigel Benn – first fought, and garnered huge attention despite no title being on the line.
The build-up to the bout, which took place at the middleweight limit of 160lb, was dominated by weight cut and rehydration clauses.
Hearn previously told BBC Sport that Benn would not entertain new weight terms for a rematch.
Eubank, 35, missed weight, incurring a £375,000 fine, but was then under the 10lb rehydration limit on the day of the fight.
He was hospitalised for two days after his win because of dehydration.
This month Eubank was fined £10,000 by the British Boxing Board of Control over “misuse of social media” in the build-up to the fight.
Eubank posted several videos of his weight-cutting process, which implied the use of a sauna.