Fernández, 25, informed Chelsea of his desire to leave earlier this summer after the club missed out on Champions League football.
Italian transfer journalist Nicolò Schira reported last week that the Argentine had agreed personal terms with Real Madrid, with journalist Giorgio Longari adding that a verbal five-year agreement was in place between player and club.
Chelsea are not under pressure to sell and do not want to lose one of their most influential performers, but the scale of their asking price reflects a willingness to listen. Madrid paid a staggering sum to sign Fernández from Benfica in January 2023, and Chelsea are demanding the same amount they spent to acquire him.
Despite agreeing terms with the player, Real Madrid have not yet submitted a formal offer and a gap may remain between what the club are willing to pay and what Chelsea are demanding. Fabrizio Romano confirmed earlier this week that no club-to-club negotiations had taken place, and that Madrid are also weighing more affordable midfield alternatives.
Fernández contributed 10 goals and four assists in 36 Premier League appearances last season, starting 35 of those matches. His contract at Stamford Bridge runs until 2032.
New Chelsea manager Xabi Alonso, who does not officially begin work until July 1, has yet to make his position on Fernández publicly known.