The two light-heavyweights went head to head for the Welshman's WBO strap in October, with Cleverly inching a split decision.
Bellew, who faces Danny Macintosh this Saturday, believes that the 25-year-old has since taken the easier options rather than give him another fight.
"I feel like I've come off the best performance of my career but I've been left to rot. I was supposed to fight in January but it didn't happen," said Bellew.
"I would have gone to Cardiff to fight Cleverly again and that would not have been a problem for me – but he doesn't want to know.
"He's taking easier options. It was a close, hard fight. I gave him my word I would give him a rematch because I didn't want to just scrape by him. Cleverly doesn't want anything to do with me but people want to see that fight."
Bellew is the current British and Commonwealth light-heavyweight champion.