Cahill, 32, has made 285 appearances for Chelsea since a 2011 move from Bolton Wanderers.
Just three of those appearances have come during the 2018-19 campaign, however, and the experienced defender has made just one Premier League outing for the Blues this term.
Cahill's contract with Chelsea will expire at the end of this season, and it is thought that the Englishman could leave Stamford Bridge at the start of 2019, with West Ham United linked with a move.
According to Turkish-Football, Cahill is Galatasaray's number one January target, with the Turkish giants determined to bring the experienced defender to Istanbul.
Cahill has won one Champions League, one FA Cup and two Premier League titles during his time at Chelsea.