'The Australian' reported that Arthur received no notice of termination nor any suggestion that he was in breach of contract.
Arthur, who had been contracted till the end of the 2015 World Cup, was entitled to three months' notice by the Australian board.
The South African has appointed a high-profile legal team Harmers Lawyers, it reported.
"I am gutted. I didn't see it coming. I can look back at it and say I've chucked everything at it. I think I leave with a lot of professional pride, I think I leave with a lot of professional dignity," Arthur had said after being axed.
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