"We're looking at fighting Andy Ruiz and we're looking at bringing it here to New Zealand," said Parker.
"We'd love to host the fight here and give back to all of the supporters but also make history.
"If the opportunity does arise that we fight for the WBO World Championship I'd take it in a heartbeat and I'd love to bring it to New Zealand."
WBO officials are due to convene in Puerto Rico on October 18 (NZT) to discuss Fury's situation and Parker's promoter Dean Lonergan will be in attendance eager to learn of the outcome.
Parker also holds the number one mandatory position for a fight for Anthony Joshua's IBF title and sits fourth in line to Deontay Wilder's WBC crown.
The 24-year-old highlighted his credentials for a world title fight when he easily accounted for Alexander Dimitrenko in Manukau on Saturday.
On Sunday he will return to his Las Vegas training base but is prepared to be patient while the various permutations around Fury's situation are clarified.
"It's just boxing," he said. "These things are happening in the background. "We just have to be patient and see what the outcomes are.
"While we are being patient we just have to push along with training, keeping fit, keeping strong and just being prepared for whatever comes our way."
In the meantime, Parker has already begun studying the form of Ruiz Junior, and is wary of the 27-year-old's punching power.
Ruiz stung him when he connected during a sparring session three-years ago but Parker believes a solid preparation would guarantee him a title victory.
"I've actually looked at a lot of tape of Ruiz, of what I could find on YouTube, and I'm excited of the opportunity to fight him and if we bring it back down here I know I'll be champion.
"Ruiz is a fighter who likes to come forward and put on pressure.
"When I sparred him in 2013 he had a lot of power. He punched me the hardest I've ever been punched and ripped my mouth and I couldn't eat for three days.
"So I know he's got a lot of power and he's got a lot of experience but I know if I have a great training camp I'll beat anyone in the world."
Parker's management are similarly excited about staging a title fight against Ruiz Junior in Auckland, with Eden Park the touted venue, which is expected to attract a global television audience of more than a hundred million people.