Should Postecoglou as expected seek new challenges when his contract runs out in a year, Football Federation Australia should nail down Arnold who is a proven winner and the perfect man to lead the Socceroos.
Arnold achieved his greatest triumph as coach when he led Sydney FC to a memorable A-League premiership-championship double.
A win on penalties over Melbourne Victory in the epic grand final at the weekend left no doubt about the Sky Blues' technical, tactical and physical superiority from day one.
It also established Arnold as one of Australia's most successful coaches, having already won a premiership and a championship with Central Coast Mariners.
Arnold is a far more qualified, composed and confident coach than he was a decade or so ago when he embarked on a coaching journey on his own after a three-year player/coach stint at Northern Spirit from 1998 and after serving an apprenticeship under Dutchman Guus Hiddink in 2005 and 2006.
He has had his critics over the years, particularly after taking over as interim Australia coach in the post-Hiddink era.
He led the Socceroos in their failed AFC 2007 Asian Cup attempt and presided over the Olyroos' fruitless Olympic Games campaign in 2008.
Club football however has galvanised Arnold's reputation and there will be no club in Australia that would not like to have him as head coach.
He took the Mariners to A-League championship glory in 2013, two years after coming within seconds of winning the grand final.
In an absorbing match at Suncorp, Arnold gave a clear demonstration of his tactical nous when his team outplayed and outmanoeuvred Postecoglou's all-conquering Brisbane Roar but lost on penalties after seeing outright victory taken away from them by a goal in the dying seconds of extra time.
Arnold is now seen as an excellent man manager and is an acknowledged tactical expert who prepares his game plans to the minutest of detail.
"Arnie is incredible at bringing a group of players together to play for each other," says his former Mariners championship-winning captain John Hutchinson, who is now a reserves coach at Seattle Sounders in the United States.
"All his players will want to win for the players next to them and also for the staff.
"Tactically, Arnie will have a plan A, B and C and will change the way his teams play with a single call . or grunt. His players will understand how to get to the opposition's third and then he will let the flair players do the rest. His attention to detail is incredible".
Fellow championship winner Patrick Zwaanswijk said Arnold had learned well from Hiddink.
"He analyses the opposition thoroughly by watching videos of their games several times," Zwaanswijk said.
"He then defines their weaknesses in defence and transition to defence and explains very clearly how they play," Zwaanswijk said. "He leaves nothing to chance."
FFA might see him as an awkward customer who is unafraid to speak his mind and Sydney are unlikely to let go of their coach in a hurry. His contract in fact has been extended till the end of 2018-2019.
Arnold is very much his own man and one of the first things he demanded when he joined the club in mid-2014 was that he be the sole spokesman on player movements.
Results always help of course but one of the reasons Sydney FC have become such a stable and smooth organisation is that Arnold has stopped the club from being a constant target of rumours and innuendo.
Arnold has often stated his desire to coach in Europe and probably realises his brushes with FFA would count against him being the next Socceroos boss, assuming he wants the job, that is.
And of course he still will be under contract with Sydney when Postecoglou's deal expires in a year.
But the Socceroos should always come first and ideally all interests should be set aside for a common goal.
I am sure the national team would remain in very good hands were Arnold to succeed Postecoglou.