The Australian newspaper said Jones agreed terms for his departure with Rugby Australia powerbrokers Phil Waugh and Hamish McLennan over the weekend.
National broadcaster ABC and the Sydney Morning Herald also said he had quit. Rugby Australia told AFP it had no comment.
Speculation has been rife that the 63-year-old would walk away after just two wins from nine Tests since taking over in January and a worst-ever World Cup performance, where Australia failed to make it out of the pool phase.
"I haven't got any job offer," Jones, who is in Britain to co-coach the Barbarians against Wales, told The Australian in an interview.
"I've been living apart from my wife because she lives in Japan. I want to spend a bit of time with her. I want to stay married. I think at 63 I don't want to get divorced.
"And then come December, I'll start to have a look and see what I'd like to coach another international team, I'd like to coach one more team. One more cycle."
Jones was hailed as the saviour of Australian rugby when he returned to the national set-up earlier this year, replacing New Zealander Dave Rennie after a string of bad results.
Fresh from inking a lucrative contract through to the 2027 World Cup in Australia, he predicted the Wallabies could win the trophy in France this year through a special "smash and grab" raid on rugby's greatest prize.
Instead the side were bundled out in pool play.
Jones has been linked with the head coach role of Japan, which he has denied.
Jones has warm relationships with key powerbrokers at the top of Japanese rugby, having previously coached the Brave Blossoms between 2012 and 2015.