Cycling Australia started interviewing the seven short-listed candidates on Wednesday and hope their choice will start in the role by March.
Sutton enjoyed massive success in the British cycling system, at the Team Sky professional road team and as British Cycling's technical director.
But he resigned as technical director before the Rio Olympics amid allegations of sexism and was also accused of making derogatory comments about para-cyclists.
An internal investigation then found him guilty of using inappropriate and discriminatory language towards track cyclist Jess Varnish.
Sutton has denied the allegations and says he would appeal.
According to Varnish, Sutton told her she should go and have a baby when she was dropped from the British Olympic program.
Sutton was then accused of calling para-cyclists gimps and wobblies.
Sutton has polarised opinion among key British cycling figures.
While stars such as track cycling great Victoria Pendleton and Varnish are strongly critical of Sutton, he has also received plenty of support from current and former riders including Tour de France winner Brad Wiggins and Olympic track champion Chris Hoy.
There is no doubt Sutton has the credentials to replace Kevin Tabotta as Cycling Australia's performance boss, but it also would be guaranteed to prompt a backlash.
Speaking about the issue at the Rio Olympics, Pendleton said "I wish we had the older brother".
She was referring to Gary Sutton, who coached the Australian women's track endurance squad at the Games.
The Suttons are Australians, with Shane working in British cycling since 2002.
Cycling Australia chief executive Nick Green would not confirm on Thursday whether Sutton was on the high-performance manager shortlist.
"We are looking for the next person to be a really strong leader of a very strong cycling system," Green said.
"Australia and Great Britain are probably regarded as the two best high-performance cycling nations.
"Great Britain are No.1 at clearly our strategy is to knock them off in four years time."
Also believed to be on the interview list is Germany's Heiko Salzwedel, who has served in a high-performance capacity in the Australian, German, Russian and British programs.
While at the Australian Institute of Sport In the early 1990's he was involved in the development of riders like Robbie McEwen, Kathy Watt, Henk Vogels and Matt White and created Australia's first UCI-registered road squad, Giant-AIS.