WBO light-heavyweight champion Cleverly defeated Bellew in a controversial bout last October and admits that he may offer him a second fight.
Cleverly said: "He looked impressive and that's an option.
"It's not ideal. If he had a world title belt then that would help, we could have an unification fight.
"It's a fight I want anyway, because I want to put the record straight. I think the last fight was a good fight and I think a second one would be as well."
Cleverly is also reportedly being lined up to meet WBC champion Chad Dawson.