Ramos hit the milestone figure of 150 appearances for La Roja in Friday night's 1-1 draw with Germany, leaving him 17 behind his former teammate for club and country.
The 31-year-old, who made his debut for the Spain senior side in 2005, is "proud" to have reached the landmark figure and now hopes to overhaul legendary goalkeeper Casillas before bowing out.
"Iker is shaking already!" he told reporters after the draw in Dusseldorf. "His figure is going to be difficult to beat. I'm proud to get here and I'm not going to throw in the towel."
Casillas retired from international duty in 2016 after 16 years' service.