Hopkins has targeted the unbeaten Cleverly should the 48-year-old come through against IBF title-holder Tavoris Cloud on March 9.
Cleverly defends his title against Robin Krasniqi a week later at Wembley Arena, and all going well, he is looking forward to fighting the sport's oldest world champion.
“It was great to read that Hopkins wants to fight me as I’ve been calling him out for a while and he’s the name that I want on my record more than any other,” said Cleverly.
“He’s a great fighter, a definite hall-of-famer, and the name that will take my career to the next level, but I’m confident in my skill and ability and know that if he fought me it would be his last fight.
“It’s my aim to unify titles and I agree with what Hopkins said about every division should have one king and not wanting to walk around with three other people carrying world titles.
“I hope he gets through Cloud and wins the title then we can look to unify the titles at the end of the year, if not, then I’d be happy to take on Cloud.”
Cleverly, 26, added: “Krasniqi is the first and only thing on my mind at the moment. It can be distracting talking about bigger fights down the line and things can go wrong in boxing as it’s only takes one punch to make or break plans.
“I’ve always said that I want to challenge myself against the best and I’m building towards that now. I’ve got Krasniqi and then (Juergen) Braehmer to deal with and then hopefully Hopkins.”
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