The Wallabies open their June Test campaign just four days later against Scotland in Newcastle, followed by a clash with Six Nations champions Wales in Brisbane on June 9.
O'Connor, who only had his first meal on Monday, is awaiting the all-clear from his hepatobiliary specialist to fly back to Melbourne.
Wallabies doctor Warren MacDonald has been in contact with the Melbourne medical team and confirmed O'Connor won't resume contact training for six weeks - placing him in extreme doubt for at least the start of the Test series.
O'Connor's loss would be a major blow to the Wallabies backline, given he was likely to start at No.10 in the absence of the injured Quade Cooper.
MacDonald also confirmed Queensland centre Ben Tapuai requires an operation on his broken collarbone and will be sidelined for three months.
- AAP