The 35-year-old stopped David Haye in five rounds in their rematch at London’s 02 Arena, dropping the former WBA heavyweight champion three times and leaving him to consider retirement.
Bellew’s trainer, Dave Coldwell, and promoter Eddie Hearn revealed they would also like their fighter to retire, given two significant purses against Haye followed him having achieved his ambitions of winning a world title and fighting at Everton’s Goodison Park.
Despite his victories at heavyweight and the fact he continues to improve, Bellew recognises his natural size compared to that of reigning world champions Anthony Joshua and Deontay Wilder means they are too big and powerful for him to challenge.
He regardless considers the less powerful Fury a worthwhile risk and believes American Ward – a world champion at super-middleweight and light-heavyweight – can be tempted out of retirement.
“It’s hard when you’ve had your defining moment in this sport. What am I chasing?” said Bellew.
“I don’t know. I like fighting and challenges, and I’ve definitely got a screw loose, so I’ll keep fighting until the screw detaches itself.
“I’m not stopping now. See if I can talk wife Rachael round and we’ll go from there. That’s my biggest fight.
“It doesn’t matter what I do I can’t beat Goodison Park.
“My first words to Haye, post-fight were: ‘Please stop’. This is a very unforgiving sport, it’s a young man’s game for the attributes Haye relies on. All the attributes he had, he doesn’t possess them. He’s an amazing fighter and will go down better than me.
“I’ll beat Andre Ward. An amazing fighter, but I will beat him.
“I’d love to knock out Tyson Fury, I really would, and I know I can flatten him. But I’m not waiting for the returning Fury to have three or four fights.”
Bellew had struggled with the death of his brother-in-law Ashley Roberts last year.
He added: “It’s been emotionally one of the worst camps I’ve had, and I’m in a room at night crying myself to sleep. It’s hard losing a brother-in-law, your missus and the family is broken.”