The Spain international is currently in his 15th campaign at the Bernabeu, with his current deal lasting until the end of next season.
However, according to AS, Los Blancos are currently against adding a further two years to the 33-year-old's terms, despite his legendary status at the club.
As it stands, the La Liga leaders are only prepared to hand Ramos a one-year extension, keeping him in the capital until 2022.
Nevertheless, the report adds that Real do not feel in any rush to reach a positive conclusion to any informal discussions, keeping the onus on Ramos to prove his worth to the first-team squad.
Ramos has previously indicated that he would like to see out his playing days at the club.