The Spaniard has just 18 months left on his contract at the Santiago Bernabeu, meaning that he could leave in a cut-price deal between £5m and £10m.
The Telegraph reports that the Blues are preparing a bid for the defender, who is yet to make his professional debut for Los Blancos.
The report also states that Graham Potter's side will face competition from RB Leipzig and Juventus for the 20-year-old, with both sides monitoring the player's progress.
Todd Boehly has made his desire to sign young players with high potential clear with the club signing the likes of Andrey Santos, Benoit Badiashile, David Datro Fofana, Carney Chukwuemeka, Cesare Casadei and Gabriel Slonina under his ownership.
Whilst Marin is yet to make his senior debut, he has impressed at Real Madrid Castilla, the Spanish giants' reserve team, and has featured for Spain at youth level.