Son has been missing in action for Spurs' last two matches, including their 1-0 Europa League semi-final win over Eintracht Frankfurt.
Speaking ahead of their clash with Nottingham Forest, Postecoglu was less than optimistic about Son's situation.
"Not really sure. It's something he's been dealing with for a while, and it's not improving, it's getting worse," he revealed.
"Rest is going to be as important as anything else with that kind of injury. So we'll give him that time. He's always eager to train, but we'll have to put him on ice for a few days and see how he responds."
