Wallabies coach Michael Cheika quit Sunday after their humiliating World Cup quarterfinal exit against England, reports said.

Cheika, whose contract expires at the end of the year, had previously indicated he would not reapply for his job if they failed to win the tournament.

After refusing to comment on his plans in the immediate aftermath of their 40-16 defeat to England, several media outlets in Australia said he had confirmed it was his last game in charge.

"Michael Cheika has confirmed he won't seek re-appointment as Wallabies coach after Australia's World Cup quarterfinal exit," rugby.com.au said.

Cheika, who narrowly avoided the axe after a horror season last year in which the side won just four of 13 tests, had come under fire from Australian media Sunday over his tactics in the tournament.

"It is no secret I have no relationship with the CEO (Raelene Castle) and not much with the chairman (Cameron Clyne)," Cheika was quoted as saying by Australia's Fox Sports website.

"I knew from the final whistle but I just wanted to give it that little bit time to cool down, talk to my people and then make it clear."

Australia's World Cup exit was a bitter end for eight squad members who are either moving to overseas clubs next year or retiring, including centurions Will Genia and Sekope Kepu, along with flanker David Pocock.

Glasgow Warriors coach Dave Rennie, a New Zealander, is seen as among the front-runners to replace Cheika.