Klinsmann has expressed interest in role through a third-party to Football Federation Australia, while the governing body has made contact with Muslin, who is understood to be in Australia, according to reports from News Corp.
It is believed Klinsmann asked a friend to initiate dialogue with the FFA, and to explain to him the level of talent in Socceroos playing pool, the team's ambition at the World Cup and the strength of the A-League.
The 53-year-old has remained club-less since being fired from the USA job 12 months ago, after a series of poor World Cup qualification results that ultimately saw the team miss a spot in Russia.
A potential issue for Klinsmann's appointment is salary, with the German believed to have been paid AU$3.3 million-per-year with the US, while the FFA only has a budget for AU$1.5 million-a-year.
Klinsmann has significant World Cup experience as both a player and a manager, having been a part of the West Germany team to win 1990 World Cup and also coaching his country to third place at the 2006 edition on home soil.
The emergence of Muslin as an option has come as a surprise, with the 64-year-old axed as an Serbian manager in late October despite guiding the team to Russia as qualification group leader - with only one loss in 10 matches.
It is understood the FFA contacted Muslin about his interest in the role when they learned he was in Australia.
Muslin is a highly-experienced tactician who started his managerial career in France's lower leagues in 1989, and has coached at clubs such as Bordeaux, Red Star Belgrade, Lokomotiv Moscow and Standard Liege.
The interview and selection process for the Socceroos job is currently being complicated by FIFA's expected intervention into the running of the game in Australia, meaning it's unlikely a candidate will be appointed until next year.