"Let's get the big fights on," said Welshman Cleverly, who is unbeaten.
Cleverly - who was speaking before Hopkins achieved his historic victory - added his name to the list of British world champions after a farcical build-up to Saturday's action in which his opponent changed from Braehmer, to Tony Bellew to Kuziemski in the space of a couple of days.
And he now wants to work with his promoter Frank Warren to target the top names in the division after taking being awarded the WBO title following Braehmer's late withdrawal.
"They're the sorts of fights I want to be involved in," he added.
"There are some big names on my radar. I've spoken to Frank and we've mentioned one or two defences.
"I think I've earned my world title because I've won the Commonwealth, British and European and a world title eliminator, the interim world title - and finally I've got the world title."
Warren agreed that Cleverly was ready to take on the best in the division.
"I like Pascal. He gave Carl Froch a great fight. But when you look at how Hopkins fought him, I thought he did enough to win that fight... I think Nathan's up there with all of them, I really do," he said.
"There are fights where he wouldn't be able to have a tear-up, but can they take what he's got? He throws really good combinations and stamps his authority on the fight from the opening bell."
Perhaps understandably, given the build-up to the fight, Cleverly looked short of his fluent best against Kuziemski - but did enough to earn a fourth-round stoppage.
"I felt quite comfortable against him, but I was still in second gear which is why I got caught with that shot in the third round - I got careless," he said.
"But overall I was very pleased with the performance. Unfortunately the ref stopped it before I could put him on the canvas. It was inevitable.
"He had a busted nose, his eye was sliced, how much more could he take? I was starting to warm up, go for my shots and move through the gears.
"It was unfortunate for me because I wanted to win more emphatically. I think the ref timed it right though, the writing was on the wall."
Warren also praised Cleverly's performance in the light of all the "aggravation" and "mental strain" he endured over the previous few days.
"You've got to take your hats off to Kuziemski, he came fight, he was a tough so-and-so. Nathan was a man on a mission and did what he had to do."
Cleverly added: "I'm only 24 and as the months go on I'm getting stronger and stronger.
"Every time I step in the ring I feel stronger and every shot I hit the guy with I felt was having an impact."
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