That's according to Spurs expert Alasdair Gold, who is reporting the Australian's name was raised inside the boardroom after the dismissal of caretaker manager Igor Tudor.
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Postecoglou was sacked at the end of last season, despite guiding the club to victory in the Europa League.
Gold stated on his YouTube channel: "I hear from sources that they briefly considered Ange Postecoglou as a caretaker coach.
"But it was very short-term that they were considered."
Spurs appointed Roberto de Zerbi as new manager, signing a contract to 2031.