The Spanish giants released an official statement after comments from Fernandez's agent, Javier Pastore, fuelled rumours that a move to the Santiago Bernabeu could be on the cards.
Madrid made their position clear, saying: "The club wishes to state that it has not made any efforts, either directly or indirectly, aimed at signing the aforementioned player."
The club added: "Furthermore, the club has no intention of pursuing such an operation."
Madrid rarely comment on transfer speculation, but said they felt it was necessary to respond out of respect for both the player and Chelsea.
"We wish to express our utmost respect for Fernandez, a great footballer whose career and quality are widely recognised, as well as for Chelsea, a club with which we maintain an excellent institutional relationship," the statement continued.
"It is out of respect for an institution like Chelsea and the principles of loyalty that have always guided our actions that the club considers it necessary to categorically deny such speculation, which is unfounded and does not reflect reality."
Fernandez's future has been the subject of growing attention after his agent hinted that a switch to Madrid could appeal to the midfielder.
"Who doesn't like Madrid?" Pastore said earlier this week. "Enzo has many friends there. I also live in Madrid."
The Chelsea midfielder, who is currently with Argentina at the 2026 FIFA World Cup, remains under contract at Stamford Bridge until 2032. Chelsea are understood to value him at around 120 million pounds and would prefer to keep him, despite reports that the player has been interested in leaving for several months.
Last season, Fernandez was left out of Chelsea's squad for two matches after admitting in an interview that he "really likes Madrid," a decision that Pastore criticised at the time.