The club captain's contract is running down this season and can commit to a pre-contract with a foreign club from January 1.
Ahead of today's clash at Chelsea, Postecoglou was asked about Son's situation and replied: "Right now all I care about is Sunday.
"I couldn’t care about people’s contracts. I couldn’t care about their situations. What I care about is Sunday and I want to make sure we have a group of players on Sunday who are ready to go out there and fight."
Of his own relationship with fans, the manager also said: "I don’t need support. I don’t worry about contracts, I don’t worry about support.
"I just want to make sure that what I set out to do, I accomplish and that is to bring success to this football club. I will work my backside off to make sure that happens. I am not going to be deterred in my ambitions or endeavour to do that and that’s what I’ll keep doing."
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