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A report from The Australian newspaper suggested Sanzaar has made the decision.
That was later backed up by New Zealand commentator Scotty Stevenson.
The Australian reported a Sunwolves spokesperson as saying the club had been asked to pay a participation fee.
It had declined to.
It was also reported no other club had been asked to pay that fee.
Stevenson tweeted the team will remain in the competition for another year, until the current broadcast agreement finishes.
The Sunwolves joined Super Rugby in 2016, alongside Argentina's Jaguares.
They have struggled over that time, having won just seven of their 43 matches.
However, they had begun looking up this year and claimed a win over the Chiefs in Hamilton.
The team is coached by former Otago and Highlanders player and coach Tony Brown.
It also has strong southern links in its playing ranks.
Hayden Parker, Tom Rowe, Josh Timu, Phil Burleigh, Jason Emery, Craig Millar, Shota Horie, Fumiaki Tanaka and Dan Pryor are all in this season's squad.
All have played for either Otago or the Highlanders.