The Netherlands international is available on a free after leaving Real Madrid this summer, and has caught the eye of the newly-promoted Serie A outfit
The Turin side are eager to add some fresh blood to their squad in order to be competitive at the highest level following their promotion to Italy's top tier last season, and head coach Giampiero Ventura sees the Dutchman as a useful addition to his team.
Drenthe came through the ranks of the Feyenoord youth academy, but left the Eredivisie side for the Bernabeu in the summer of 2007.
Nevertheless, the 25-year-old failed to live up to the high expectations at the Liga champions, and was released on a free transfer this summer after loan spells at Hercules and Everton in the past two seasons.
He has since been linked with clubs such as Feyenoord and Galatasaray, but could now be on his way to Italy instead following Torino's interest.