Cleverly has made five successful defences of his WBO light-heavyweight title, but he would like a super fight in the United States, or an all-British showdown with Froch to propel his career in to the big time.
Cleverly's promoter Frank Warren claimed on Tuesday that Froch had turned down a £2.5million offer to take on his 26-year-old fighter. Warren even says he promised Froch that he would not have had to put his IBF and WBA super-middleweight belts on the line for the fight, for which Cleverly would have to drop down one weight division.
Although Cleverly is a world champion, Froch claims he is not good enough to face him in the ring - a claim that has clearly riled the Cefn Fforest fighter.
Cleverly accused Froch of being too scared to fight him and also laughed off the Midlander's claim to be the best British boxer of all time along with Lennox Lewis.
"I have a lot of respect for Froch, but the idea of him being the self-proclaimed best British fighter ever is an absolute joke," Cleverly said.
"That's disrespectful to the likes of Joe Calzaghe, who would have boxed Froch's head off.
"Let's face it - he is slow, robotic, and he is claiming he is the best British fighter ever.... it's just idiotic.
"And to disregard me as a worthy challenger, that's the biggest thing... it's ridiculous.
"This is someone who has been outboxed by Andre Dirrell, Andre Ward and Jermain Taylor. He was beaten by Mikkel Kessler once."
Cleverly looks to have given up any hope of fighting Froch, who seems intent on setting up a rematch with Ward instead.
"If I'm being honest, I don't think it will happen not because of me, but because of him," Cleverly added.
"His arrogance will take him down another route.
"He doesn't want to fight me because with my speed, ability and naturally bigger frame, I would be too much for him."
Cleverly will make the sixth defence of his belt on August 17 at Cardiff's Motorpoint Arena, although the identity of his opponent is still up in the air.