Parker's former promoter Dean Lonergan told RadioLIVE last week that fighting Hunt would be the perfect comeback fight for the former WBO heavyweight champion - who has lost his previous two bouts.
The 26-year-old lost to Anthony Joshua and Dillian Whyte respectively
Hunt - who has one fight remaining on his UFC contract - has lost three of his last four fights inside the Octagon, but more importantly has never fought a professional boxing fight in a 19-year combat sports career.
But when asked about the idea, Parker gave a good reason to why that would never happen.
"He's a great fighter, I'm a boxer, and he's a UFC fighter, but we're family so we can't fight each other," he told the AM Show.
The pair are distant cousins, have Samoan roots, and both born were born and raised in South Auckland.
Parker said an announcement on his next opponent is due soon.
"We're looking at fighting at the end of the year, hopefully back in New Zealand, and we'll hopefully make an announcement soon.
"We're looking forward to climbing back to the top and fighting for the titles again."
Parker was speaking at the Eat My Lunch headquarters for its millionth lunch for children in need.
One in four Kiwi kids live in poverty, and thousands go to school every day without lunch, and Parker was happy to devote his time to people in need.
"I want to help give lunches to those who are less fortunate and those who don't have lunches at school because it will help them with learning and sports and give them energy throughout the day.
"It has been great seeing everyone here, joining in helping out and trying to make a difference. Everyone is working well together, and we're looking forward to making this millionth lunch."