The Manchester United shot-stopper was included in Vicente del Bosque's provisional 30-man squad for the FIFA World Cup earlier this month.
The party must be cut to 23 by June 2 and Costa's race against time is the subject of much interest.
The Atletico Madrid forward has battled hamstring problems recently and broke down inside the first 10 minutes of Saturday's UEFA Champions League final against Real Madrid.
De Gea hailed Costa's rise in the 2013-14 season and said the forward, who is crucial to Spain's hopes, should be given time to prove his fitness.
"He is important for the team. I think we should wait," De Gea is quoted as saying in AS.
"I met him several years ago. He’s exploded this year and he makes a difference.
"He's had an impressive year and now we have to wait. We want him to be 100 per cent."
De Gea is yet to make his Spain debut and is behind Iker Casillas and Pepe Reina in the pecking order.
But the 23-year-old is hoping to make his maiden appearance in pre-tournament friendlies against Bolivia and El Salvador.
"I want to debut," he added.
"I know the level of our goalkeepers is high and there are players of many levels.
"I'm trying to make the most of my opportunity and hopefully I can.
"There is a lot of speculation about who will go to Brazil and who won't. It's to be expected."
Spain will play the Netherlands – the side they beat in the 2010 World Cup final – Chile and Australia in a tough Group B in Brazil.
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