Cahill has been left out of both of Chelsea's matchday squads so far and is understood to be deemed surplus to requirements by new boss Maurizio Sarri, who has switched to two central defenders as opposed to Antonio Conte's system of three at the back.
Antonio Rudiger and David Luiz appear to be Sarri's preferred centre-back partnership as things stand, while Andreas Christensen, Cesar Azpilicueta and Ethan Ampadu provide further options in the middle.
Cahill's contract at Stamford Bridge expires at the end of this season, and Turkish outlet Fotomac reports that Chelsea could look to cash in on the England international during the final week of the European transfer window.
Turkish champions Galatasaray are understood to be leading the race for the 32-year-old as they look for an alternative to original target Jason Denayer, who joined Lyon from Manchester City instead.
Cahill joined Chelsea in January 2012 and has since gone on to make 282 appearances for the club, helping them to every major honour.