Ramos, 35, ran down his contract and, according to Spanish newspaper Marca, was unable to agree an extension after Real offered him a one-year deal on a 10% pay cut which he rejected.
Ramos signed for Real from Sevilla in 2005 for a then 27 million euros, a record fee for a Spanish defender.
Making 671 appearances and scoring 101 goals, Ramos was made captain in 2015 after the departure of goalkeeper Iker Casillas.