While Hearn is determined to make the fight happen, DeGale will still contest for a world title at London's O2 Arena on October 11 should Froch refuse the offer.
"In an ideal world I'd put DeGale and Froch in a ring together," said Hearn.
"Domestic fights work. DeGale is a ready-made domestic challenger for Froch and the mandatory challenger for his IBF title."
An eighth-round knockout of George Groves at Wembley Stadium back in May ensured that Froch kept his WBA and IBF super-middleweight titles.
On the same night, DeGale, who has an Olympic gold medal to his name, impressed on the undercard after beating Brandon Gonzales in four rounds.