The 32-year-old has been struggling with a back injury of late and was ruled out of his side's one-day tour of India.
However, the New South Wales batsman could now return for the Aussies' first Ashes Test against England in Brisbane starting on November 21.
"Michael is progressing well and recently recommenced batting in the nets," Australian team physiotherapist Alex Kountouris said in a statement.
"At this stage we are aiming to have him fit to play the second round of the Sheffield Shield, but we have not ruled out the possibility of him playing the first round of the Shield season if he makes better than expected progress. We'll continue to monitor him closely."
New South Wales will start their Sheffield Shield campaign against Tasmania on October 30 and will take on Victoria at the MCG on November 6.