Arthur, a South African who in 2011 became the first foreign head coach of Australia's top team, is asking for $4 million (R40m) in compensation or his job back after being fired last month on the eve of the Ashes series in England.
He was replaced by former test batsman Darren Lehmann.
After more than five hours of talks at the Fair Work Commission failed to reach an agreement on Wednesday, both sides agreed resume negotiations on July 31.
Arthur says, "Although we didn't come to an outcome on Wednesday, I'm pretty confident that there was enough goodwill in the room for us to continue talks next week."