Cleverly beat Shawn Hawk on his American debut last night to defend his WBO light-heavyweight title.
The Welshman has been touted alongside fellow champions Tavoris Cloud and Beibut Shumenov as a possible opponent for 47-year-old Hopkins.
The 25-year-old Briton says that he would welcome the chance to fight the veteran boxer.
"That would be a great fight," he told BoxingScene. "Bernard was a great fighter. I think it would be a great fight for the light-heavyweight division.
"I'm a world champion. I've got an exciting style. It would be a good gel of styles.
"Bernard is technically excellent and with my excitement - that would be an interesting fight and one I would like to be involved in."
Hopkins said last month that he has not decided whether he would fight again but is thought to be interested in another world title attempt.