The former Hoops boss is available after his dismissal by Nottingham Forest earlier this month.
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And Postecoglou has been mentioned as a candidate for the Celtic job after Brendan Rodgers' resignation this week.
But the Scottish Sun says the Aussie isn't seeking an immediate return to football and favours a spell out of the game to recharge his batteries.
Postecoglou won five major trophies during his time with Celtic - a record that includes two league titles, the Scottish Cup and two Scottish FA Cups.