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Arnold's contract expires at the end of the cup in Qatar, with the 59-year-old non-committal about his future.
But Arnold is making a compelling case to be offered a fresh contract after becoming the first Australian-born coach to lead the Socceroos to a World Cup win.
Australia's 1-0 triumph against Tunisia in Doha has placed the nation on the cusp of qualifying for the knockout phases of the cup for only the second time.
Beat or draw with Denmark on Wednesday (0200 AEDT Thursday) and Arnold will join his Dutch-born mentor Guus Hiddink in 2006 in steering the Socceroos out of their group.
Socceroos striker Mitch Duke says Arnold deserves to be offered another deal.
"That's completely on him to see if he wants to continue," Duke told reporters.
"But for me, personally, I have obviously loved working under Arnie.
"I love the way he coaches, I love the atmosphere he creates in camp and if that he wanted to do that, to continue on, I back him 100 per cent.
"But that is obviously an individual thing for him.
"He has been doing it for this whole journey, it has not been easy.
"But I am sure every lad in this team would like to see him continue on."
Arnold's position was in danger during Australia's troubled qualification for the cup before Football Australia backed him publicly in late March this year.
And Duke said the culture created by Arnold was crucial in Australia's first win at a World Cup in a dozen years - only Dutch duo Hiddink and Pim Verbeek, in 2010, had overseen a victory at football's showpiece tournament.
"One of the keywords is family. And belief. And that is what Arnie has created in this group over this four-and-a-half-year period," Duke said.
"We are a family. The lads definitely feel that vibe every time we come into camp, it's a brotherhood.
"It has been brilliant, everyone backs themselves and they back their mates.
"And we all feel like we could go to war with each other and that is the belief and trust in that family environment that we have built over these years.
"It has got us through some tough times when the outside maybe wrote us off a little bit."
