The Lions have been keeping tabs on the Serbian international and are keen on reinforcing their defence over the winter transfer window.
Ivanovic will have six-months remaining on his contract in January and Galatasaray would be able to sign him on a free transfer.
Chelsea are unlikely to offer the experienced defender a contract extension considering Antonio Conte has dropped Ivanovic since switching to a 3-4-3.
The 32-year-old has been left out of the squad for four of the Blues last five games despite being a first-team regular up until the tactical change made by the Italian coach.
Galatasaray are currently third in the Turkish league just three points behind the leaders and have been linked with Ivanovic over the last few transfer windows.
Ivanovic has made a total of seven appearances in all competitions for the Blues this season.