Cadena Cope says everything is settled over a new agreement - with just the date of the signing ceremony to be settled.
The captain will ink terms to 2021 and see his salary raised to €12m. The deal will mean Ramos will be 35 when inside the final year of the contract.
Ramos had pushed hard for a deal to 2022, but Real president Florentino Perez resisted, particularly given the defender's wage demands.
Over the past week, Dani Carvajal and Isco have also extended their contracts.