The Spanish captain is entering the final 100 days of his current deal at the Santiago Bernabeu and, with no agreement reached, the centre-back would be a free agent as of June 30.
Real Madrid's wage bill has been put under strain due to the pandemic, leading many players to accept a 10% pay cut, something Ramos is reluctant to do without the promise of a longer contract on the table.
It is believed that Ramos will have to make a decision soon, as the contract offer from Perez has an expiry date where Real Madrid will decide to move on and start building their squad for next season.
Ramos has openly expressed his desire to stay with Los Blancos until the end of his career, but has been linked with a move to the likes of Manchester United and Paris Saint-Germain if he leaves the Spanish capital this summer.
The 34-year-old, who has featured only 20 times in all competitions for the Spanish giants during an injury-affected 2020-21 season, joined Madrid in 2005 and has gone on to make 670 appearances for the club.