The Black Sea Storm are reported to be in talks with the Blues over making the Germany international’s stay permanent.
Marin joined the Turkish Super League club on a one-year loan with a future buyout clause over the summer and has established himself as a first team player in the side.
The 26-year-old winger has one goal and three assists in all competitions for Black Sea based side this season.
Trabzonspor are currently in 10th place in the league on 20 points after 15 games and coached by Sadi Tekelioğlu.
Marin is one of two Blues players who joined a top-flight Turkish club on a temporary move.
Nigerian international Kenneth Omeruo joined Kasımpaşa on a one-year loan with a future buyout clause option over the summer.