Haye continues to recover from an Achilles injury sustained during their last fight in London
Tony Bellew's trainer Dave Coldwell says they will look for other fights if David Haye's recovery from injury is prolonged.
Bellew triumphed over the former world heavyweight champion at the beginning of March by securing an 11th round knockout in London's O2 Arena.
With Haye picking up the injury during the fight, Bellew was able to bide his time before winning the bout and promoter Eddie Hearn said after the fight that he could market the Liverpudlian as a heavyweight.
"David Haye's fans want a rematch but Haye isn't someone that can give us a date," he wrote. "With an active fighter like Joseph Parker or Deontay Wilder, we can make a date.
"We don't know if Haye is ever going to fight again."
Bellew spoke emotionally after his victory over the 36-year-old about the fact that he had secured his children's future and he will now decide if he wants to fight again.
"There's a few names on the hat. If you're stepping up to heavyweight and going for a world title, Parker is not a giant height-wise. He's a little bit green, and Tony's brain is fantastic. Wilder is long and dynamic, but technically he's the weakest [of the heavyweight champions]."
Tony Bellew (right) speaks with David Haye after his victory during the heavyweight contest at The O2. Image: Nick Potts/PA Wire/PA Images