The Turkish Super Lig broadcaster LigTv state that the Trabzonspor are preparing to hold talks with the Italian manager.
LigTv go onto state that Trabzonspor president Muharrem Usta is keen on appointing Di Matteo for the upcoming season.
Trabzonspor are currently managed by Hami Mandıralı who was appointed earlier this season.
Di Matteo stepped down as manager of Schalke after just seven months in charge of the Bundesliga side. The Italian manager previously won the UEFA Champions League with Chelsea back in 2012.
Trabzonspor have endured a turbulent season and currently find themselves in 10th place with 33 points in 26 games.
Hami Mandıralı’s side defeated Sivasspor by a 1-0 scoreline in their previous league game. The Black Sea Storm take on Gaziantepspor this weekend and could move up to ninth place with a victory.