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Fish and Game Central South Island said eyewitnesses reported seeing an angler land a 24.9kg (55lb) brown trout in the Pukaki-Ohau A canal near Mt Cook.
If confirmed, it would be a new world record for a brown trout.
According to the International Game Fish Association website, the present record is a 19.1kg (42lb 1oz) fish caught in the same canals in 2013.
But Fish and Game field officer Rhys Adams said confirming the potentially record-breaking monster trout was proving difficult.
"Secrecy surrounds the catch and we want to solve the mystery," he said.
"This is an amazing fish and we would love to confirm it but at the moment, the lucky angler is keeping quiet.
"Because of the international significance of the catch, we would like to hear from anyone who has more information or details."
Fish and Game communications advisor Richard Cosgrove said some details were starting to emerge.
"Witnesses say the fish was landed after a two-and-a-half-hour fight," he said.
"Once he had the fish landed, the angler wrapped it in his shirt to keep it cool before getting ice from a nearby salmon farm and rushing it to a taxidermist.
"He also got it weighed on certified scales to confirm that this was the fish of a lifetime.
"We have been told the whole story, along with photos, will emerge once the trout has been mounted."
The Mackenzie basin hydro canals have a well-deserved reputation in New Zealand and overseas for consistently producing huge trout.
The canals are easy to access, flow through spectacular high country scenery and are open all year round.
But it is the number of huge trout living there which attracts thousands of anglers every year, making the canal network the country's most popular freshwater sports fishery.
According to Fish and Game's latest canal harvest survey, anglers made approximately 43,800 daytime visits to the canal fishery during the 2015-2016 season.
Adams said those anglers were catching big trout.
"Rainbow trout have the most impressive seasonal catch figures," he said.
"Around 30 per cent of rainbows are trophy size, between 10 and 20 pounds, with 9 per cent classed as 'exceptionally large' - that's over 20 pounds."
He said he hoped the monster brown trout catch could be confirmed.
"It's much rarer to catch an exceptionally large brown trout - only about 1 per cent of browns caught in the canals fall into this category, so it would be nice to make this official," he said.
"The size of these trout just reinforces how good New Zealand's trout fishing is. If we can confirm this brown trout record, then the next thing is setting a new world record for rainbow trout."
The present rainbow trout record is 21.77kg (48lbs) for a rainbow trout caught in Canada in 2009.