A potential bout between the two Kiwi heavyweights was hypothesized earlier this week by Parker's former promoter Dean Longergan in an interview with RadioLive.
Lonergan was under the impression it would be a good comeback fight for Parker, who has suffered back-to-back losses in his two most recent outings.
"That's the only true local fight that would have any appeal to the New Zealand fans," Lonergan said.
However, Parker told TV3 he wasn't interested in a fight with Hunt - who is his distant cousin.
"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," Parker said.
Parker's current promoter, David Higgins, told the Herald last week that he had "three irons in the fire", including a ready-made option in the United Kingdom, but that it was Parker's preference to fight again in New Zealand.
The Australian-based Hunt was hoping to land a spot on the card for UFC Fight Night Adelaide in December, which would see him leave the promotion in front of a home crowd. A few potential opponents for him have circulated online, but the UFC was yet to confirm they would get Hunt on the card.