Former Tottenham manager Harry Redknapp backed Postecoglou to be the next Spurs boss last week.
"I said to a few people I thought he would be a frontrunner," he told BBC Scotland. "If I was looking for somebody, if I was the chairman of Tottenham, he would be right at the top of my list.
"I'm sure it'd be a big blow to the Celtic fans to lose him. But I don't know, he's leaving a great club in Celtic but maybe the Premier League, the contract, the wages and what goes with it might be hard for him to turn it down if he does get offered.