The Liverpool shot-stopper recently expressed a desire to edge ahead of the 21-year-old in the pecking order for the competition in June.
However, Courtois - who has been his nation's number one since Marc Wilmots took charge in 2012 - has advised his rival to adopt a similar approach as his Spanish counterparts and shelve his individual ambition.
He told Sport/Foot Magazine: "In Spain, I hear no goalkeeper saying they're aiming for the place of Casillas. Not De Gea, not Valdes, not Reina. It's the opposite - they back Casillas.
"Simon can say whatever he wants, but I think I've already saved enough points for Belgium and I'm playing good games for Atletico. He has to stay humble and respectful."
The Belgian youngster - on loan in the Spanish capital from Chelsea - has earned 14 caps for his country.