The Cefn Fforest WBO light-heavyweight champion is looking to go up against the big names in boxing and his trainer and father Vince has revealed that, if dropping down to 168lbs was the only way he could fight unified IBF and WBA super-middleweight champion Froch, then he would do it.
Froch, who defeated long-term rival Mikkel Kessler on points at London's O2 Arena on Saturday to avenge his defeat in Copenhagen three years ago, has always said that he would end Cleverly's career in boxing if they ever met up.
That has irked Cleverly snr who claims his son, who is unbeaten in 26 professional fights, has done more than enough in his career at the age of 26 to warrant a meeting with 35-year-old Froch or WBA champion Andre Ward.
"Firstly I think it's totally unnecessary for Froch to talk about Nathan [Cleverly] the way he has," he told the South Wales Argus. "He's the biggest name in British boxing and he should be above that kind of thing.
"But if that's the way he looks at it, that he'd only fight Nathan at super-middleweight, then our response is done, he's got himself a deal and we'll very happily accept that challenge.
"It would be a one-time thing, Nathan would bully Carl at super-middleweight and for one fight we'd be happy to step down a weight.
"People throw all sorts of accusations at Nathan about not taking the big fights, but we don't make the fights. Nathan is desperate for the biggest names out there. We even contacted Frank Warren (Cleverly's promoter) about challenging Andre Ward. So if Carl thinks we wouldn't consider a fight at 168, he's dead wrong."