Fernandez, 25, joined Chelsea from Benfica for a then Premier League record fee back in January 2023, signing an eight-and-half-year deal.
Following a disappointing season for the Stamford Bridge club, Fernandez’s agent, Pastore, has now confirmed that they are looking to leave.
"The player is calmly thinking about the national team, he is playing in a World Cup, he is very close to reaching the round of 16," Pastore told Marca.
"He is only thinking about that, and we are looking at possibilities to leave Chelsea, but there is nothing firm or confirmed at any club."
When asked about Fernandez’s admiration for the city of Madrid, Pastore added: "He has many friends there, and he is very close friends with Julian Alvarez, and in the end, whenever they can spend time together, they are together there.
"And I also live in Madrid. Every time he travelled, he travelled to see me and to sort out work-related matters, but besides that, who doesn't like Madrid? I never even played in Madrid. I even live there."
Chelsea value Fernandez at £120 million, a fee that has since been justified by the sales of Elliot Anderson, Sandro Tonali, and Mateus Fernandes.
Real Madrid have been heavily linked with the move for the Argentina international, but it remains to be seen whether they would be willing to pay such a fee.