Unfancied Australia won two matches for the first time at a World Cup finals before bowing out in the round of 16 against Argentina.
Arnold was contracted through to the end of Australia's Qatar campaign but captain Mat Ryan said he hoped the 59-year-old would remain in charge.
"I think results speak for themselves and he’s become the most successful Australian manager ever with the results that he’s gotten and he’s been riding a real wave of success and momentum," the goalkeeper told reporters after arriving in Sydney.
"Obviously I have faith in the organisation to make that decision and Arnie himself has to be wanting and willing to continue as well.
"For us it would be great if we could continue to have him there with us."
While Football Australia congratulated Arnold on Sunday, the governing body has not commented publicly on the coaching question and said it would undertake a thorough review of the World Cup.
Arnold has said he will consider his options after a "good break", while his agent told Sydney's Daily Telegraph multiple clubs and international federations had shown interest in Arnold's services.
Defender Harry Souttar said the man known simply as 'Arnie' in Australia had an excellent relationship with the players.
"I think the biggest compliment I could pay to him is I think every one of the lads would go out there and run through a brick wall for him he’s that type of manager," the Scotland-born centre back said.
"I think he’s the best man manager I’ve worked under and he just gets the feeling of the players and as a group of players we all love to play for him."
