Martin, 39, was sacked after just 17 games in charge at Ibrox, leading Rangers to the worst start to a season in 47 years.
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Rangers have been looking to hire a replacement for the former Southampton boss for the past couple of weeks, and were understood to be keen on bringing Muscat, 52, back to the club.
The Shanghai Port manager spent the 2002-23 season at Rangers, but according to GIVEMESPORT, has turned down the chance to return.
It’s understood that Muscat had concerns about the club’s recruitment model and he has now pulled out of the race.
The report adds that Rangers are insistent complexities of Muscat finishing the Chinese Super League season led to them backing down.