Porto goalkeeper Casillas has been the country's first-choice keeper since 2002 but De Gea is considered favourite to start after a solid season for Manchester United.
"De Gea is no longer the future but a strong contender," Casillas told Cadena Cope radio.
"It's clear that all of us that are here, we think that we can play.
"We are 23 players that play as starters for important clubs and we all believe that we can help the national team but deciding who starts is the coach's job."
Spain coach Vicente del Bosque will not make a decision of who will play between the posts until June 13, when his team begins its European Championship campaign against the Czech Republic in Toulouse.
Del Bosque did confirm that de Gea will start against Georgia in Tuesday's friendly in Getafe. Casillas started against South Korea in last week's 6-1 triumph.
Asked if he thinks he will start at Euro 2016, Casillas said, "That is a question for Del Bosque."
De Gea, 25, made his senior debut in June 2014 in an international friendly and was included in Spain's World Cup squad but did not feature.
He has made eight appearances for Spain but only started in three Euro 2016 qualifiers for the European champions, with Casillas as the preferred number one in the last two years.
De Gea almost became Casillas' replacement at the Bernabeu Stadium last summer when the latter left for Porto but United and Real did not complete the deal before the transfer deadline.
There is a lot of attention on Casillas and De Gea in the Spanish media.
"I know there are 40 cameras focusing on what I do, any gesture that I have towards David will be taken out of context to be used in TV shows," Casillas said.
However, Casillas says that there is a healthy competition in the team.
"What I really like is that, besides being 35, I have the same hunger, enthusiasm and I continue to compete," he said.
"Now I'm with De Gea and with (Sevilla goalkeeper) Sergio Rico and it's going well."
Asked about his future in the national team, Casillas said, "I will decide after the tournament."
(Reporting by Cindy Garcia; editing by Amlan Chakraborty)
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