Froch said that he was the "number one" boxer in Great Britain after his points victory over Mikkel Kessler, but Cleverly believes that the IBF super-middleweight holder has shown 'disrespect' to his fellow domestic fighters.
The 26-year-old told The Sun: "Carl's been disrespectful to past British champions.
"He's also been disrespectful to me by saying that 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. He knows that and that's why he's gone as quiet as a mouse about the fight."
Cleverly is currently preparing to defend his world title against Russian Sergey Kovalev in August.