Former Manchester City prospect Robertson has two caps for Australia, enjoying minutes in friendlies against Argentina in China and Ecuador in Sydney.
Robertson wasn't in Popovic's first squad for games against China and Japan and the coach's understanding was he was not eligible to be picked, which Football Australia later indicated was due to a paperwork issue.
But Popovic confirmed Robertson had chosen not to make himself available for selection at all ahead of World Cup qualifiers against Saudi Arabia and Bahrain.
"Look, that sits in his hands now," Popovic said.
"If he wants to play for the Socceroos he needs to make himself available.
"It's not an Alex issue, it's an Alex decision on what he wants to do. So if he wants to make himself available for the Socceroos, then we can look at whether we select him.
"At the moment we don't have that option.
"I don't know the exact reasons or what he's thinking at the moment, but I just know that he's not available for selection."
The 21-year-old, whose father and grandfather both played for the Socceroos, is also eligible for Scotland, Peru and England.
A FIFA rule change in 2020 allows players to switch allegiance if they have played no more than three competitive matches at senior level prior to them turning 21.
When asked whether Robertson was focusing on his club career or looking to play for another nation, Popovic said it was a question for the player.
"We've had people that have spoken to him. We understand where he sits at the moment in terms of his decision," he said.
"He's a young man that's made a decision. We have to respect that decision.
"He's young, trying to make his way in football, he's playing regularly, so we'll keep monitoring him, and we'll see what happens in the future."
Robertson hasn't indicated publicly that he is looking to switch allegiances and Popovic wouldn't be drawn on whether he would be disappointed if the midfielder looked elsewhere.
"You have to respect the shirt, the badge," Popovic said.
"You have to respect the honour of playing for the Socceroos and we also have to respect the fact that everyone can make their own choice and their decision, and right now, his decision is not to make himself available.
"That does not mean he was being selected. Let's make that clear as well. He's a young player that's coming through.
"But we know he's a talent. We have many young, talented players that are trying to forge a career in Europe.
"We will watch him. We'll monitor him, as we have throughout the year - we watched all his matches - continue to do that, and if the opportunity comes that we can select him, we'll make that decision then."
