Rogic broke a bone in his hand during Sunday's 1-0 loss to Jordan in Al Ain and had the injury assessed upon the team's arrival in Dubai on Monday.
The Celtic attacking midfielder has also been nursing a knee problem from before the tournament and wore a bandage with a guard on his left hand during Tuesday's session.
Rogic only ran four or five laps away from the main group in running shoes before ending his session early.
Despite the light workload, Socceroos staff remain confident the 26-year-old will take to the field at the Rashid Stadium.
Assistant coach Rene Meulensteen says the results of an assessment undertaken by a specialist in Dubai on Monday will determine Rogic's availability.
"Every player's health is paramount to everything," Meulensteen said.
"I think there is a few scenarios they're looking at at the moment so we'll have to get the full scale of what we've got to do with that one ... when he's got the ultimate results of whether he can keep playing or not."
The Socceroos injury woes don't stop there with striker Andrew Nabbout and fullback Josh Risdon also struggling with groin complaints.
Nabbout undertook running drills alongside hamstrung forward Mathew Leckie on Tuesday and appears to be recovering well from the groin injury picked up on the eve of the Jordan clash.
Risdon's hopes of recovering in time for Friday's match look less encouraging with the Western Sydney Wanderer sitting out the entire training session.
"I don't think he'll be fit," Meulensteen said.
"He over-stretched himself in the abdominal area and these are very bad injuries that you can't really do anything about.
"You can't inject them or tape them or whatever it is. He's going to need review but again, I think he'll be a doubt for Palestine."
Injuries have been a constant theme throughout the build-up to Australia's Asian Cup defence.
Aaron Mooy, Daniel Arzani and Martin Boyle were all ruled out before the tournament started while Leckie remains unavailable as he recovers from a hamstring tear.
With Leckie sidelined, if Nabbout, Rogic and Risdon are ruled out of Friday's match it will leave Graham Arnold with just 16 fit outfield players to select his starting XI from.
