Cleverly's camp have made an offer for an all-British super-middleweight clash, but Hearn has claimed that 'the Cobra' has no interest in the possible bout.
In-fact, Hearn went as far as saying that Cleverly's offer to face the IBF world champion was little more than "a publicity stunt".
"They could offer £10m, the fight isn't going to happen," said Hearn.
"The money's irrelevant. Anyway, the offer they made us was probably half of what I'd pay Carl for the same fight.
"I told Carl about it last night and he laughed. Carl feels sorry for Nathan and thinks he's a good young fighter. It's a publicity stunt."
Froch recently announced that US boxer Yusaf Mack will be his next opponent at his home arena in Nottingham.