Justin Langer told Cricket Australia (CA) that he quit as national team coach because he realised he no longer had the support of several players and board members, according to a report in The Australian on Sunday.
The newspaper said it had obtained a copy of Langer's Saturday resignation email to CA boss Nick Hockley.
"Last night I was offered a short-term contract until the end of the T20 World Cup in Australia, with the sentiment of 'going out on a high'," Langer wrote, according to the newspaper.
"After careful consideration I have decided not to accept this contract renewal, and as a result I believe it is in everyone's best interests for the Australian cricket team to begin the next chapter immediately."
"If media reports are correct, several senior players and a couple of support staff don't support me moving forward, and it is now apparent the CA board, and you Nick, are also keen to see the team move in another direction. I respect that decision."
Reuters could not independently confirm the accuracy of the letter.
Langer took over as national coach in 2018 in the wake of a ball-tampering scandal and most recently presided over a 4-0 defeat of England in the Ashes Test series.
Australia also won last year's Twenty20 World Cup for the first time under Langer but there have been reports of player discontent over his coaching style.
He has already been mentioned as a candidate for the vacant England head coach job following the departure of Chris Silverwood.
According to The Australian report, Langer left with his head held high.
"Whilst it is not up to me to judge, I hope Australians respect what has been achieved over the last four years in Australian cricket," he said.
"From day one I believed it was possible to both win and play the game in the spirit that is now expected from our supporters."
"For the last four years it has been proven this can be achieved and I am very proud of the team for their efforts on and off the cricket field. I hope we have made Australians proud and earned respect from countries around the world."
"I am grateful that today, I am going out on a high. Hopefully a good job has been done and I wish the team every success for the future."