The Merseysider injured his right hand during his 11th round stoppage victory over Haye at The O2 earlier this month and is believed to have suffered a torn capsule which might need an operation.
"I have spent time with my surgeon so he could assess what is going on and what we do going forward," Bellew exclusively told Sky Sports. "I will just leave it with him, he knows best."
"I have damaged my hand. In there is some kind of tear; you have some sort of capsule over each knuckle and I've split it.
"I've also got a fracture in the hand, but when people just say 'you've broken your hand', essentially I have but it is a fracture.
"It's going to take a little bit of time, but we'll take it from there."The healing process starts now! With my surgeon @mike_hayton #BestHandSurgeonInTheBusiness pic.twitter.com/ZSzb1wz2fZ
— Tony Bellew (@TonyBellew) March 14, 2017
World title fights against WBC champion Deontay Wilder and WBO king Joseph Parker have already been discussed, while Bellew could grant a rematch to Haye, who is also recovering from injury.