Sari joined Galatasaray in February 2014 from Eskisehirspor for €700,000.
The versatile footballer has been left out of the squad in recent weeks following the return of Sabri Sarioglu to the Galatasaray squad.
Sarı was also heavily criticised for his performance against Arsenal in the UEFA Champions League.
Newly appointed Trabzonspor manager Ersun Yanal previously worked with Sarı at Eskisehirspor.
Galatasaray who are planning to reduce to side of the squad will be willing to offload Sarı in January.
Sarı has made 8 appearances for Galatasaray this season.