Kovalev stopped Cleverly inside four rounds in August to claim the WBO light-heavyweight crown, but the former titlist has admitted that he wants the opportunity to try to redeem himself.
The 26-year-old told BBC Radio Wales Sport: "There's only one fight that I want and that's the rematch. I don't care about the money. Am I going to get it? Who knows.
"I'll try my best to get it, I'll go to America for it. It's not about the money for me - it's not about the pay-day - it's about having that chance to get my title back."
Cleverly's defeat was the first of his 27-fight professional career.