Madrid have scheduled a farewell ceremony for their longtime captain in the presence of club president Florentino Perez on Thursday.
Ramos, 35, wanted a new two-year deal to stay at Madrid, but sources told ESPN that Perez was not prepared to break his policy of handing only one-year contracts to players over 30.
Conversations between Perez and Ramos have been ongoing throughout the past year and continued into June. However, neither party was prepared to compromise.
Despite reports to the contrary, sources told ESPN that Ramos did not demand a pay rise to stay at the Santiago Bernabeu.
Ramos, who made 671 appearances for Madrid, scoring 101 goals, has still not made a firm decision on his future and is not expected to announce his next destination at Thursday's goodbye event.
ESPN revealed recently that Manchester City are the front-runners to land his signature, although there are other options on the table.
The Premier League champions are prepared to offer a two-year deal until the summer of 2023. From there, depending on performances and Ramos' own plans, the defender could either continue for a third season at City or take up an option to join Major League Soccer side New York City FC, who are also owned by the City Football Group.
Ramos is a direct petition from City coach Pep Guardiola. The former Barcelona boss values the experience he would add to his squad and the competition and guidance he would provide for younger centre-backs Ruben Dias and John Stones.
Ramos turned 35 in March, but sources have told ESPN that City manage data that suggests he's still able to perform physically at the level of a player "aged between 28 and 30."
ESPN first reported on Jan. 4 that City were monitoring Ramos' situation. Guardiola's insistence has been the key to them continuing to follow developments with Madrid.
However, the player's camp aren't ruling anything out, with several clubs expressing interest in recent months.
Madrid signed Ramos in 2005 from Sevilla, paying his €27 million release clause.
He soon became a key member of the side and in 16 years at the club has won five La Liga titles, four Champions Leagues, four Club World Cups, three European Super Cups, two Copa del Reys and four Spanish Super Cups.
Ramos made just 21 appearances for Madrid in all competitions last season as Los Blancos ended the campaign without a trophy, missing out on the league title to rivals Atletico Madrid on the final day of the season.