Former WBO king Parker, 29, has not fought since he beat Derek Chisora by split decision at the AO Arena in Manchester.
The heavyweight rivals will rematch one another at the same venue over seven months later on Saturday night, where Fury is also expected to be in attendance.
Fury was ringside when Parker beat his cousin Hughie to win the WBO belt back in 2017 and the two have since become close friends, with the latter revealing the former treats him like a ‘younger brother’.
However, that hasn’t stopped the New Zealander from wondering how he might fare against the undefeated Gypsy King, as he revealed the thought of fighting his friend has crossed his mind before on several occasions.
“I’ve always said it would be great to fight him because I see him as the best heavyweight there is at the moment,” Parker told the Daily Mail.
“I’m not really part of his plans, he’s got plans to fight this person or that person, he might retire or carry on for another 10 years. No one really knows.
“He looks after me, treats me like a younger brother and helps me with my career, my fight that’s coming up.
“He’s been very generous so I don’t think it’s a fight that will ever happen.
“But I’m always supporting him, always there to watch his fights and cheer him on.”
But Parker insists his mind is firmly fixed on what’s in front of him rather than thinking about the future.
“A good win will give me a great start to 2022,” he added.
“I just want to be involved in big fights and fight the best out there, to prove I am the best, one of the best.
“If I lose this fight, I’m not sure where I’d go after that. So I’ve got to be fully focused on who’s in front of me.”
In regards to Chisora, Parker isn’t expecting anything new, although he reckons ‘he’s going to be a lot fitter’ than before.
“I’m anticipating a very similar fight,” Parker continued.
“He’s going to be a lot fitter. He’s going to try some new moves, and obviously with Coldwell and the team they have, he’s got a great environment to be in.
“I don’t think there’s a lot he can change with his style as he’s done it for years and years, but it only takes little adjustments to make a big difference in a fight.”
He added: “I’m confident I’m going to win.
“I’m confident I can beat him up and I’m confident I can knock him out, I just need to land at the right time, pick my shots, listen to my trainer and go out and perform.
“I know I can perform better than I have in the past, I’m just going to go out and prove that.”