The Football Association have started their search for a new manager following Gareth Southgate's decision to end his eight-year reign on Tuesday in the aftermath of last weekend's Euro 2024 final defeat against Spain.
Postecoglou has joined England Under-21s coach Lee Carsley, Newcastle manager Eddie Howe, former Chelsea bosses Mauricio Pochettino and Graham Potter and ex-Bayern Munich chief Thomas Tuchel on the FA's list of potential candidates.
After a largely impressive first season with Tottenham, who finished fifth in the Premier League, the attack-minded Postecoglou would be an intriguing choice to replace Southgate, who was widely criticised for his cautious tactics.
However, the 58-year-old stressed his attention remains on Tottenham, who opened their pre-season with a 5-1 win at Scottish Premiership side Hearts on Wednesday.
"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 said.
"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)."
Postecoglou coached Australia from 2013 to 2017 -- taking them to the 2014 World Cup -- and twice won the Scottish Premiership with Celtic before moving to Tottenham in 2023.
Asked if he would consider a return to an international job, 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."
England's first match after the Euros comes on September 7 when they face the Republic of Ireland in the Nations League.
The FA could appoint Carsley as an interim manager if they have not found a permanent successor to Southgate by the time they play Ireland.
