The 25-year-old has spent the past month away on international duty with Australia, whose World Cup campaign was ended with defeat to Peru on Tuesday afternoon.
Rogic has now been given a fortnight off by Rodgers to recuperate ahead of the 2018-19 season, meaning that he will not be back in time for the meeting with Alashkert in Armenia on July 10.
"He'll have two weeks off from now, so he'll be back when we arrive home from the first leg," he told reporters. "He'll be back training on the 12th of July.
"He won't be playing in the first leg, it's a long season for us and he's just off the back of World Cup preparation and World Cup group stages, so he'll have two weeks free and then come back fresh and ready for hopefully another exciting season."
Rogic started all three of Australia's group matches at the World Cup without completing a game.