"That's the point where we started this great friendship and sort of brotherhood."
Talking of his closeness to the Traveller fighters, he said: "It is like a tribe. In New Zealand we have Maori, we have a very diverse community. Everyone sticks with their tribe. Tyson, there's Billy Joe, there's Andy Lee, I feel like I fit right in - not necessarily their tribe - but we understand each other. We get along very well and I feel very fortunate and blessed to train alongside them. It's something new and something different. It's always great to learn from cultures and tribes."
Yet victory over Chisora could propel Parker towards reclaiming a world title and, in spite of the friendship with Fury, it is a prospect Parker relishes.
"I've always said I would love to fight the best, and him and Anthony Joshua are the best in the world. He's made it clear to me that he will never fight me and he doesn't see a reason to fight me.
"I respect that. If I want to fight him, I can keep calling him out. If he doesn't want to fight, that's his own decision."
As the official announcement of Fury vs Joshua approaches, Parker added: "I'm a little biased, I'm close to Tyson. I back Fury and I feel he could get a stoppage. But if I had my choice, I would like to rematch Joshua."
Parker lost a unification fight with the Briton in 2018.
But back to Chisora, and the date with destiny next Sunday.
"I'm looking forward to it," Parker said. "Andy is a very good teacher. My style hasn't changed a lot, but it's improved and looks a lot better. I feel like I'm at the beginning of my career again."
Book the Parker v Chisora Earlybird Pay-Per-View for $39.99 on Spark Sport.
The Sunday Telegraph -Telegraph Media Group