The Argentine has long been a name on Mourinho's list of preferred reinforcements for the position, with the Chelsea midfielder considered the standout option among those put forward by the Portuguese coach.
Fernandez made his interest in a future move to the Spanish capital clear on March 30, in comments that caused considerable disruption at Stamford Bridge and saw him temporarily removed from first-team activities.
"I would like to live in Spain. I really like Madrid, it reminds me of Buenos Aires. A player lives wherever they want. I get by in English, but I'd be better in Spanish."
Fernandez was later pictured at the Mutua Madrid Open tennis tournament, further fuelling speculation over a potential move to Real Madrid.
His agent, former player Javier Pastore, is aware of Real Madrid's interest and his client's wishes, though the deal is not expected to be as straightforward as the Marc Cucurella transfer given the fee involved.
Chelsea have not closed the door on a sale, with manager Xabi Alonso unwilling to retain any player not fully committed to the project, though the London club will not make Fernandez's departure easy either, reports Marca.
Chelsea have consistently valued Fernandez at no less than €120m, the same fee they paid Benfica for him in the winter of 2023 following the Qatar World Cup.
Real Madrid would ideally complete another rapid operation similar to the Cucurella deal in order to wrap up their squad business as quickly as possible this summer.
Should the Enzo Fernandez deal fall through, Mourinho's recruitment search continues to focus on alternatives, with West Ham United's Mateus Fernandes among the names that most appeal to the Portuguese coach.
The 21-year-old is known for his composure on the ball, precision in execution, and ability to cover ground and reach the opposition box.
That profile fits closely with Real Madrid's search for players capable of breaking down deep, rigid defensive blocks through creativity, dynamism and an ability to find space between the lines.
Fernandes remains highly regarded in England despite West Ham's relegation from the Premier League this season, and has attracted interest from several suitors ahead of next season.
A call from Mourinho, however, could completely change the picture surrounding his future.
Fernandes is one of Mourinho's favoured options to strengthen the midfield, though far from the only alternative to Enzo Fernandez under consideration.
In recent hours, the name of Ayyoub Bouaddi, one of the standout performers of the World Cup so far, has also emerged strongly as a fresh option on Real Madrid's radar.