The Hibernian winger went off with a lower-leg injury during the win over St Mirren on Saturday.
The 29-year-old has scored five goals in 19 internationals and become a key player for Australia in recent seasons.
The Socceroos begin their World Cup campaign against France on November 22 before taking on Tunisia and Denmark.
Hibs manager Lee Johnson said: "He's had a scan and he's currently in Manchester getting that scan reviewed by a specialist and a consultant. I would hope that by this time on Thursday we will have a clear and acute diagnosis and prognosis on the injury.
"We are just positive with him, we all live in hope that he's in a good place. He seems to be moving well, although the scan is showing something, it seems, which is why he has gone to the specialist.
"He is presenting well, which gives us a lot of hope. But at the same time we need real expert opinion."