Parker has had just two defences of his title in 2017 since claiming the world title with a majority decision victory over Andy Ruiz Jr last December.
The 25-year-old improved to 24-0 with victories over Razvan Cojanu in May and Hughie Fury in September.
Parker told ESPN that he was close to fighting Bellew earlier this year but the timing didn't work out for him.
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"I'd love to fight Tony Bellew," Parker said. "We had discussions to fight when David Haye pulled out of the fight but we weren't in a full camp so not able to jump in and fill his place.
"I feel like if I had a great camp and prepared for Tony Bellew I could put on a great fight and beat him. Hopefully we can make something happen.
"But again it comes down to both teams being happy. I know he's a massive draw card so we would have to sit down and negotiate how we're going to split things but I feel it's a great possibility to fight in 2018.
"He's a great fighter but he's a cruiserweight coming up to heavyweight. I have better skills and a little bit more power."