The Black Sea Storm are reported to be interested in signing Marin on loan with a future-buyout clause.
Marin who joined Trabzonspor on loan from the Blues over the summer has established himself as a first team regular and a fan favourite at the club.
The 26-year-old has one goal and four assists in 18 appearances for Trabzonspor this season who are currently in 10th place but have a game in hand.
Marin left Chelsea after struggling for playing time under Jose Mourinho but it remains to be seen what plans current head coach Gus Hiddink has for the Germany international.
The Trabzonspor winger 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.