Final interviews to succeed the sacked Michael Beale at Ibrox are taking place this week with Belgian Clement and ex-Gers defender Muscat both believing they are in with a good chance of landing the job.
Scott Parker was also considered as a possible option but sources close to the former Fulham and Bournemouth boss say he is taking his time over a return to the dugout.
Ex-Chelsea manager Frank Lampard was removed from the shortlist after a negative backlash from supporters.
Former Australia international Muscat, spent one season at Ibrox as a player during the 2002/03 campaign, clocking up 22 appearances for the Gers.
Known for his no-nonsense, tough-tackling style, Muscat has since gone on to carve out a respectable management career in Australia and more recently in Japan.
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The 50-year-old succeeded Tottenham boss Ange Postecoglou as manager of Japanese side Yokohama F. Marinos, leading them to the J1 League title in 2022.
His heroics prompted Postecoglou to talk up the idea of Muscat one day following him to the Premier League.
The Spurs boss exclusively told talkSPORT: "Watch out for him, he'll be another one that comes across.
"[He'll be] another Aussie that comes across here and breaks down some barriers."
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Meanwhile, Belgian coach Clement remains on Rangers' radar after leaving his post as Monaco boss at the end of last season.
Clement spent 18 months at the Principality club and despite a promising start, failure to take Monaco through the Champions League qualifiers and into the group stage, ultimately cost him his job as his side went on to post a disappointing sixth-placed league finish last season.
The Belgian, who had a stint at Coventry City during his playing days, found managerial success in his homeland, winning the top-flight title with Genk and twice with Club Brugge.