According to the Spanish newspaper, Madrid have moved to reward the player for his remarkable showing at the 2018 FIFA World Cup in which he led the Vatreni to the final to take home the tournament's Golden Ball award.
It is understood that Modric will be placed on the same pay scale as captain Sergio Ramos and will make around €10m per year, an improvement on his current €8m.
Italian Serie A side Inter have shown a great deal of interest in signing the 33-year-old midfielder this summer, with the player's wife and agent reportedly offering her husband to the Nerazzurri.
Modric is also believed to have expressed his intent to join the side and follow former teammate Cristiano Ronaldo to Italy.
Madrid, however, were desperate not to lose two of their star players in the same window and had previously stated that any suitors looking to take the Croatian off of their books would have to cough up €750m in order to activate his release clause.
They planned a Friday meeting with the playmaker and, as reports in Spain would have it, all parties have emerged from the sit-down happy.
Inter were quite hopeful over the possibility of landing Modric in what would have been a sensational switch but they're set to be sorely disappointed, given the reported developments over in Spain.
"The company has shown to work consistently, they are trying to put everything into place," manager Luciano Spalletti was quoted as saying last week. "It is clear that a player like Modric would be important for anyone, let alone for us...I keep dreaming with the fans."