Santos, 19, has recently broken into the first team at Corinthians and is highly regarded in Brazil.
The defender will see his current contract expire in 2020, however, and according to Marca, Madrid are keeping a close eye on the development of the teenager with the view to a future move.
Santos is also a five-time Brazil Under-20 international, who has made 14 appearances for Corinthians this term.
As for Madrid, the reigning European champions have faced criticism in recent weeks following a run of four matches without a win in all competitions.
Next up for Julen Lopetegui's side is a home game against Levante on October 20.