South African Arthur was dumped after a meeting with Cricket Australia chief executive James Sutherland in Bristol, reports said. A source confirmed the news to AFP.
"Cricket Australia will hold a media conference with James Sutherland and (high performance coach) Pat Howard in Bristol tonight to discuss the coaching structure of the Australian team," Cricket Australia said in a statement.
Queensland coach Lehmann, who is in England coaching Australia A, is the firm favourite to replace Arthur, whose contract was due to run until the end of the World Cup in March 2015.
Arthur, the first foreign-born coach of the Australian team when appointed in November 2011, appears to have paid the price for a poor Champions Trophy campaign and a lack of discipline within the team, which came to a head with a David Warner punch-up incident earlier this month.
Sutherland was furious and demanded the team crack down on bad behaviour.
Warner was fined Aus$11,500 ($11,000) and suspended until the start of the Ashes series for punching England batsman Joe Root in a Birmingham bar during the Champions Trophy.
Several others players were with him in the bar in the early hours of the morning, raising concerns about the culture inside the Australian squad
It followed vice-captain Shane Watson, James Pattinson, Mitchell Johnson and Usman Khawaja all being disciplined during the India tour this year after failing to submit feedback requested by team management.
Arthur courted controversy by sending the players home midway through the series.
Australia play the first Test against England in Nottingham on July 10 and former Test batsman Mark Waugh said the timing of Arthur's sacking was not good.
"At the end of the day the players have got to be responsible as a well but Cricket Australia are obviously looking for more direction from their coach," he told Sky News.
"There's definitely been issues within the squad with team unity and there's a lack of experience there, so it just hasn't been working. It's a very dramatic decision at such an important time.
"It's going to put a lot more pressure on (skipper) Michael Clarke who has been under enough pressure himself with his back injury. So it's not an ideal situation."
The Ashes squad is due to meet for the first time in Taunton in England on Monday, for their first pre-Ashes tour match against Somerset beginning on Wednesday.