Moana Pasifika bid and the Fijian Drua have been chosen as NZR's "preferred partners" to join the new-look competition in 2022, alongside the existing five teams from New Zealand and five from Australia.
Kanaloa Pasifika claimed New Zealand Rugby breached its own rules by backing Moana Pasifika when the group did not take part in the formal tender process.
"Regardless of how they call that - whether it's a proposal or a bid or not - Moana Pasifika has certainly gone out in the public and discussed the fact that they are putting in a bid or going to put in a bid, that they are the successful bid," argued Kanaloa CEO Tracy Atiga.
"We want a fair process to come through...it's shocked a lot of people."
In a statement provided to RNZ Pacific last week, New Zealand Rugby (NZR), stood by its selection process.
"We understand Kanaloa Pasifika is disappointed and are engaging with them directly on any concerns. We stand by our process which was rigorous and fair."
"We're not in discussions. We certainly had a response from New Zealand Rugby in regards to our complaint that we put through their official New Zealand Rugby complaints mechanism, and the response that we received from New Zealand Rugby was insufficient as far as we're concerned."
Kanaloa Pasifika served New Zealand Rugby with legal notice last week, giving it 14 days to withdraw and retract its decision to support a rival Pacific Island Super Rugby bid.
"They denied some of the allegations or assertions that we had in our complaint and so what we've done is we've acted on our instructions that we would go to a legal letter which we've done," Atiga said.
"It's unfortunate that it's come to this, to be fair. It's not what we had hoped for. We would really have liked to have spoken to New Zealand Rugby about the fact that they had an opportunity to do the right thing and retract their decision that they made - probably out of haste, which is fair.
Moana Pasifika will take on the Māori All Blacks next month in a match viewed as an important step towards their Super Rugby goal.
Tracy Atiga said the fixture was another example of blurred lines between New Zealand Rugby and the Super Rugby aspirants.
"Moana Pasifika steering group was always set up under the mandate that they would put together a team to play the All Blacks and the Māori All Blacks...you've got an organisation like New Zealand Rugby Players Association (NZRPA) who stood up that particular steering group.
"New Zealand Rugby also provided their support behind the feasibility study that the group put forward to actually look at whether a sixth team for Super Rugby would actually be viable and of course here we are today, New Zealand Rugby deciding that they were going to put forward Moana Pasifika as the successful bid.
"Now the issue that we have is that Moana Pasifika did not at any stage enter a formal bid."
The Kanaloa group stressed they had no issues with the Moana Pasifika: "We are Pasifika people and we will never have issues against our own people".
But Atiga said it was inappropriate for New Zealand Rugby to use the NZRPA's endorsement of a group that they helped set-up to justify selecting Moana Pasifika as its 'preferred partner'.
If NZR does not change its stance by next Tuesday, Kanaloa Pasifika Rugby said it would file proceedings with the high court seeking an injunction to the tender process.
"This team was set up to be a Pasifika team for Pacific Island nations players - not New Zealand rugby players and that's our biggest concern."
"It's about making sure our Pasifika people are represented fairly at that level and if we want change for our Pasifika community - especially our players - then we need to make sure that we challenge these processes where the systems dont work for us...and the process that has had us miss out for 25 years."