As soon as Jurgen Klopp made the shock announcement that he would be quitting as Liverpool coach at the end of the Premier League season, citing burnout, Postecoglou’s name was raised as a possible replacement. Partly because of how strong an impression he has made in his first seven months at Tottenham Hotspur, but mostly because everybody knows he’s a Liverpool tragic at heart and the gig at Anfield is probably his dream job.

He picked the Reds as a kid because all of his mates went for Manchester United. He grew up reading stories about Bill Shankly and the ‘Boot Room’ at Anfield, and when he coached against them in an exhibition match in 2013 at the MCG, he couldn’t hide his giddiness.

So began a week of feverish speculation, which ended on Saturday night on the blue side of the city, with Postecoglou’s Spurs once again coughing up points at the death after an injury-time Jarrad Branthwaite strike earned Everton a 2-2 draw. Finishing off games is a recurring problem; Tottenham have now drawn or lost 10 games in the league this season but scored first in six of them. As Postecoglou said after their FA Cup defeat to Manchester City last weekend, Spurs are nowhere near the finished article.

To be clear, Postecoglou is going nowhere. By all reports, a deal is as good as done for Bayer Leverkusen boss Xabi Alonso to make a romantic return to the club he once played for at the end of this season, and he might do that with a Bundesliga title in the bag, with his side currently one point ahead of Bayern Munch on the German table. If not him, then Brighton’s Roberto De Zerbi is apparently Liverpool’s preferred back-up option.

In any case, and even accounting for the romance factor, Postecoglou would almost certainly refuse to entertain it. The timing is all wrong.

Unlike at Celtic, where he was on a 12-month rolling contract, Postecoglou has signed a four-year deal with Tottenham. That in itself was an enormous vote of confidence in him, but he has also just been heavily backed in the transfer market, with chairman Daniel Levy – often criticised for his spendthrift ways – bringing in €25 million defender Radu Dragusin (who turned down Bayern Munich), forward Timo Werner (on a shrewd loan-to-buy deal, if they want him for €17 million) and young gun Lucas Bergvall (who turned down Barcelona and will join in the summer) during a window in which their rivals did little business.

Postecoglou has indeed shown a ruthless streak in moving onto his next challenge when it presents itself, and often leaves his teams behind without saying a proper goodbye – but he is also very loyal, and has no reason to turn on a club that has shown so much faith in him. With another Aussie in Scott Munn the chief football officer, Mile Jedinak on the coaching staff and Johan Lange now on deck as technical director, Postecoglou is starting to properly shape the club in his image.

He also does not leave jobs half-finished. Postecoglou has done that only twice before in his career, and both in rather extraordinary circumstances. During his wilderness years, after that interview on SBS, the only job he could get was at Greek third-division side Panachaiki. After nine months in charge, he had them second on the table and in ominous form – until a new chairman tried to meddle with the football department and Postecoglou resigned immediately out of principle. Had there not been an ownership change, they would have challenged for the title.

And yes, Postecoglou did quit Melbourne Victory in 2013, after just one season, but he did so very apologetically. The opportunity to coach the Socceroos with a mandate of dramatic tactical and philosophical change was something he could not turn down; in some ways it was his destiny.

This isn’t that. The lure of Liverpool – even if they did come knocking – would not be strong enough to convince him to abandon his project in north London, especially since the early signs have looked so promising.

If he guides Tottenham to some form of success in the coming years, bigger clubs than even Liverpool may yet come for Postecoglou. If and when that happens, it should not be a surprise. For now, though, the work at Spurs continues.