It had been suggested that former WBO cruiserweight champ Enzo Maccarinelli is prepared to step down a division to challenge his fellow Welshman but Cleverly knows he is in demand as a new champion and will consider all options.
"You never know what could happen, but at the moment I’ve got bigger names on my radar," Cleverly told BBC Wales Today.
"I’m a big target out there now. I’ve got the world title and once you’ve got the world title people are going to start calling you out and want to fight you.
"I’m prepared to take on all comers and I’m ready for the big names. I really want the big names in the division.
"Tavoris Cloud is an appealing name, he’s an American name. He’s an undefeated fighter and he’s got the IBF version of the world title. He’d be a great fight.
Cleverly added: "I think I’ll end up having one or two defences of the belt and then we can look at one of those big names then."
May 24, 2011