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Parker, the former WBO heavyweight title holder, was in the southern town last week taking in the sights while his management team met local officials.
"I don't want to jump the gun. I mean we're looking at all options on the table, but it'd be great here, wouldn't it?" Parker’s manager David Higgins told Newshub.
Higgins said the boxer’s British promoter Eddie Hearn had sanctioned the idea of Parker fighting in New Zealand, one of the very few places a bout might be permitted due to the ongoing Covid-19 pandemic.
Auckland, Rotorua and Wellington were other possible venues being considered, Newshub reported.
Queenstown Lakes Mayor Jim Boult was convinced the resort had a strong case, and he hoped the funding from the Government’s tourism recovery package could be used to make the fight happen.
"We've had some initial discussions about it. I think it's a really, really good opportunity.
"It's just the sort of thing we need happening in the district."
Any fight would be in late August or early September, and Parker’s possible opponent has yet to be named.