The 33-year-old is a free agent after leaving Zenit St Petersburg over the summer.
According to Gazzetta dello Sport journalist Nicolo Schira, he was approached by the Ibrox club but rejected their advances.
Claudio #Marchisio has rejected a bid from #RangersFC. #transfers— Nicolò Schira (@NicoSchira) September 5, 2019
Marchisio left Juventus after 13 years in Turin last summer, making more than 300 appearances for the Italian giants.
However, he was released midway through his two-year deal in Russia after featuring just 15 times for the club an in injury-hit campaign.
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