On Monday, Haye was forced to withdraw from their December 17 bout after undergoing a minor operation on his arm, and the two-weight world champion has suggested that the rematch can be rescheduled for either March or May.
However, Bellew has questioned whether his rival can be trusted to be ready for either of those months, with the Liverpudlian saying that he intends to fight during the early part of 2018.
The 34-year-old told Sky Sports News: "Ideally I'd like to take a bout before. I want to stay busy, I've been known my whole career as an active fighter. I will have been out of the ring for a year, and that's not good for me. This is a job, I've got a family to feed.
"Maybe David will take an interim fight, and I'll take one too. Maybe, down the line, we meet again. I do want to face David Haye - I want to put it to rest. I've always been a massive underdog. People said I was crazy [before the first fight] but look what happened."
Bellew had hoped to face WBO heavyweight champion Joseph Parker on December 17, but the New Zealander has said that he will not be ready for a return to the ring in four weeks' time.