The 26-year-old forward only managed to score four goals in the 2021-22 Premier League season and is one of several Chelsea attackers being linked with a move away from Stamford Bridge.
Newcastle United have been strongly linked with a move for the Germany international, whose contract at the Blues does not expire for another three years.
Defensa Central claims that Los Blancos are keeping a close eye on the player’s situation with a view to potentially signing the Ex-RB Leipzig man.
Real Madrid were said to have been interested in a move for Werner in 2020, but due to the financial implications of the coronavirus pandemic, Bernabeu chiefs ended their interest.
Werner has scored 23 goals and 21 assists in 89 appearances in all competitions for Chelsea.