Cleverly slams 'disrespectful' Froch
Having avenged his 2010 defeat by Mikkel Kessler at The O2 in May, Froch said: "In Great Britain I'm number one. It's between me and Lennox Lewis, depending on how far you are going back."
But Cleverly, 26, insists that Froch has disrespected both him and the great British boxers of past eras by assuming the title of Britain's finest ever fighter.
"Carl's been disrespectful to past British champions," Cleverly, who has challenged Froch to step up in weight for a British showdown, told The Sun.
"He's also been disrespectful to me by saying I'm not a worthy challenger. But he's only interested in staying at super-middleweight and fighting smaller guys coming up to his weight."
"I'd beat Carl Froch," the Welshman added. "He knows that and that's why he's gone as quiet as a mouse about the fight."
Cleverly takes on Sergey Kovalev at Cardiff's Motorpoint Arena on August 17, while Froch is in negotiations to set up a super-middleweight showdown with Commonwealth champion George Groves.
"I'm confident that if I fight Groves, I will beat him," Froch told the Nottingham Evening Post. "The guy's not ready for me. He might be one day, but I doubt it. If he fights me, he's going to get beaten."
Groves sparred with Kessler in the build-up to Froch's points win in London, but Froch insists that he bears no grudge against the Londoner.
"I've got nothing against George Groves. It's hard for me to have anything against any other fighter," Froch insisted. "When they talk rubbish it's just to build the fight up and make some money because it's business. I do my talking with my fists.
"I don't know if the fight is going to happen. It may or may not happen before Christmas. There's nothing definite in boxing."