The Football Association is on the hunt for a new England boss after Gareth Southgate announced his decision to end his eight-year spell in charge, two days after defeat to Spain in the Euro 2024 final.
Australian Postecoglou is reportedly one of several coaches under consideration - along with the likes of England Under-21s boss Lee Carsley, Pep Guardiola, Eddie Howe, Mauricio Pochettino, Jurgen Klopp, Graham Potter and Thomas Tuchel.
Postecoglou, who was born in Greece, had a spell in charge of Australia before taking the Celtic job in 2021.
The 58-year-old, though, stressed his immediate attentions were on preparing Spurs for the new Premier League campaign, with his side having opened their pre-season with a 5-1 win at Scottish Premiership side Hearts.
"I am at the start of pre-season and am the Tottenham manager, so I have got nothing else (on my mind) but trying to bring success to this football club," Postecoglou told Sky Sports News.
"Until I do that, there is no point in me thinking about anything else.
"I had a nap this afternoon, so I have no idea what is going on (with the speculation)."
Asked if he would consider a return to an international job in the future, Postecoglou said: "I enjoyed my time (with Australia). I had four great years.
"We won the Asia Cup and qualified for the World Cup, but with all these things there is always a natural end, and I thought it was a natural end for me there.
"I loved coaching the national team. In the future, who knows? Five years ago I was in Japan, and now I am in the Premier League."
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