Neil Lennon was suspended from his role as Hibs manager on Saturday (AEDT) after a major fallout with players, staff and club chief executive Leeann Dempster.
Lennon looks unlikely to return to the job and an ESPN report claims Arnold has expressed interest in taking over at Easter Road.
Arnold, who has only been in charge of the Australia for six months, oversaw the disappointing AFC Asian Cup quarter-final exit after a shock loss to the UAE on Saturday.
The 55-year-old is the most successful coach in A-League history, with three premiership wins and two championship victories including the double, while in charge of Sydney FC in 2017.
If he was given the job at Hibernian it would leave Football Federation Australia in a precarious position with both their men's and women's senior national teams without a coach.
Arnold took over in his second stint as Socceroos boss after the 2018 FIFA World Cup, on a four year deal, and was earmarked by the FFA as the man to guide Australia through a successful Asian Cup title defence as well as qualification for the 2022 World Cup in Qatar.
However, the 55-year-old has been on the end of stinging criticism from fans for the side's performance in the UAE, with Australia only finding the net in two of their five Asian Cup games.
There are strong ties between Arnold and Hibernian with key Socceroos squad members Mark Milligan, Jamie Maclaren and Martin Boyle on the club's books.
Hibernian were 3-1 winners overnight in their first match without Lennon in charge, with academy head Eddie May and Grant Murray taking over as interim managers.
May indicated post match that he did not want the role on a full-time basis.
