The 19-year-old Spaniard was beaten twice against Barcelona last weekend but pulled off some impressive stops from the likes of David Villa and Pedro to keep Atletico's defeat down to a 2-1 scoreline.
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He impressed again at the Mestalla on Wednesday when he helped Atletico become the first side to take any points off Valencia this season, when they drew 1-1.
"Everyone's seen what he's been doing and praising his performances," Real Madrid's number one keeper told reporters.
"I don't know him personally but he has been doing very well. Watching him reminds me a lot of when I started 11 years ago.
"Between us all we have to look after him. He has a long road in front of him, and when he least expects it he will get a call up to the national team."
The Spanish youth international was recruited into Vicente del Bosque's preliminary 30-man squad for the World Cup finals in South Africa, but missed the cut behind Casillas, Victor Valdes and Pepe Reina.
He has made a huge impression since debuting as a substitute for Atletico in the Champions League last September, and jumped from the B team to undisputed first choice as the side went on win the Europa League and reach the King's Cup final last May.
One interested observer on Wednesday was Manchester United manager Sir Alex Ferguson who missed his own side's League Cup tie at Scunthorpe to be at the Mestalla.
Valencia are United's next Champions League opponents but Spanish and British media speculated on Thursday that Ferguson was there to cast his eye over De Gea.
