While Gers chiefs have met with former Sheffield Wednesday manager Danny Rohl and Ole Gunnar Solskjaer, they're now in advanced talks with Muscat.
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The former Gers fullback is being lined up for a November return to Ibrox, which is when the Chinese season concludes.
Muscat has a year to run on his Shanghai contract and Rangers face paying around £1.5m in compensation.
Muscat has already earmarked his former No2, Neil McCann, to take charge as a caretaker for the coming weeks before he becomes formally available, says the Daily Record.
Gers are turning to their former defender after ex-manager Steven Gerrard withdrew from talks on Saturday.