Rugby Australia chief executive Raelene Castle has declared she is going nowhere despite public calls for her to be moved on from Australian rugby's top office.

It comes as the 49-year-old repeatedly refused to answer questions during a prickly radio interview on Wednesday.

The former Canterbury Bulldogs executive on Tuesday flatly dismissed calls from powerful Australian rugby identities, including former coach Alan Jones, that she should resign after a period of unprecedented turmoil for the sport in Australia.

The post-mortem into the Wallabies' quarter-final crash against England has turned its attention to Castle after former coach Michael Cheika fell on his sword less than 24 hours after Australia's elimination from the World Cup.

The humiliating loss at the hands of the long-time rival has put the spotlight on the front office, but Castle turned the attention back on Israel Folau and his ongoing legal battles contributing to the early exit.

"I certainly don't think it's helpful," Castle told ABC's Radio National.

"I think when you've got a player who chooses to put their views in front of the views of the team and we end up with headlines and people writing things about Rugby Australia as opposed to writing about the rugby, that's never helpful. Of course, it's not."

Folau's unlawful termination case against Rugby Australia and Rugby NSW will be heard from February 4, unless mediation meetings scheduled in December can broker a settlement between the two parties.

Folau is also seeking an apology from Rugby Australia and the reinstatement of his $4 million contract with the Wallabies and NSW Waratahs.

Seven News reported on Tuesday night that Jones has again piled pressure on Castle and Rugby Australia chairman Cameron Clyne to resign after a disastrous campaign.

The pressure has been further heaped on Castle and Clyne after Cheika dramatically revealed he has no relationship with Castle and next to no relationship with Clyne.

Cheika's grenade during his resignation announcement in Japan came before the team returned to Australia on Tuesday morning where captain Michael Hooper and Wallabies icon David Pocock both refused to blame Cheika for the failed campaign, despite the coach's selections, game-plan and strategies all coming under fire.

Hooper, however, was unable to answer if it was possible for the team to succeed at the tournament when Cheika and Castle had no relationship.

Cheika and Castle have both admitted their relationship essentially broke down when Rugby Australia handed down its high performance review at the end of 2018, where it was recommended that Cheika retain his job — but have to suffer answering to newly appointed director of rugby Scott Johnson.

Castle admitted on Wednesday her relationship with Cheika broke down because of the appointment of Johnson. Johnson has now been given the lead role in Australia's review into the mistakes made during the Tokyo 2019 campaign.

In a prickly interview with host Hamish Macdonald on ABC breakfast radio, Castle:

— First tried to sidestep a question about when she last spoke to Cheika before being called on her failure to answer the question,

— Repeatedly refused to directly address questions about if she regrets the appointment of Johnson and if the appointment undermined Cheika; and

— Defended the decision to allow Johnson to lead the review into the failed campaign, despite his newly created position emerging as an obvious point of friction in the team's operation.

Castle at one point butted heads with Macdonald over the hosts repeated pushes to get the top administrator to answer why Johnson will carry out the review, and not an independent figure who would also investigate the impact Johnson's appointment had on the team.

When asked, "Why even have the review," Castle responded:

"Could I just finish, could I just finish.

"Because actually the point is that there was a review last year. What we're talking about is a campaign review to look at why the campaign was not successful."

Castle refused to directly address questions about the impact Johnson's appointment had on Cheika and the team this year.

"We had to make a change," she said of the decision to create a director of rugby role.