Marin has been on loan at Trabzonspor since the beginning of the season but is understood to be unhappy with the situation at the club.
The Lions general security Fatih İşbecer is currently in London and the Sabah newspaper claims that he is in talks with Chelsea over the possibility of a January move for Marin.
The 26-year-old winger has one goal and four assists in all competitions for Black Sea based side this season who are currently in 10th place but have a game in hand.
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.