Outgoing head coach Michael Cheika says the next man to coach the Wallabies rugby team should "definitely" be Australian.

Cheika told reporters at Sydney Airport Tuesday, on his team's return from the Rugby World Cup in Japan, that he backed an Aussie as his successor.

"I think definitely we should be pushing for an Australian coach," he said. "It's not up to me but I think we should be backing and supporting Australian coaches wherever possible."

Australia coach Michael Cheika watches as his team warm up before the Rugby World Cup quarterfinal match at Oita Stadium between England and Australia in Oita, Japan, Saturday, Oct. 19, 2019. (AP PhotoAaron Favila)

Australia coach Michael Cheika watches as his team warm up before the Rugby World Cup quarterfinal match at Oita Stadium between England and Australia in Oita, Japan, Saturday, Oct. 19, 2019. (AP PhotoAaron Favila)

New Zealanders Dave Rennie, currently coaching Glaswegians in Scotland, and Japan head coach Jamie Joseph have been named as prospective successors to Cheika, who stepped down after Australia's 40-16 loss to England in the World Cup quarterfinals.

Cheika said he had no regrets after stepping down after five years as head coach. He had indicated before the World Cup that he would not seek to continue if Australia didn't win.

"We came second last time (at the 2015 World Cup)...and I figure (after) four years you've got to come first next time," he said. "You can't call it and then change your mind afterwards because that's genuinely what we wanted to do: was go there and win."

Cheika, who has complained of a lack of support from Rugby Australia, said there would be "no excuses, no nothing.

"That's the way I've always operated and that's the way I'll continue to operate going forward."

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