The 23-year-old's sole appearance for his country came in a friendly win over Costa Rica last November, but he was called up for the World Cup this year and was named in new coach Luis Enrique's first squad for this month's UEFA Nations League matches.
A poll conducted by Marca after the match showed nearly half of the fans asked wanted Kepa to take over in the first team for the next game.
Although Kepa himself insists he ignores any such surveys, he is prepared to contest De Gea for the position going forward.
"Being in the squad is already a reason for joy. We all want to be here and we all want to play; I work for that," he told AS.
"We'll meet the coaching staff in the first few days and get ourselves going, because we have two big games ahead.
"It's a question for the coach. What I will do is work, although obviously we all want to play.
"The coach will decide the best thing for the team, but in the training sessions I'll try to put in the effort, for the good of the group most of all.
"All players work to compete and to play. The coach decides and we accept whatever it is, always with good harmony.
"De Gea is a great goalkeeper and the goal is perfectly covered with him. The World Cup was how it was, we came back too early, but I don't pay attention to polls or what people say. I try to isolate myself and focus on myself."
Kepa became the world's most expensive goalkeeper when he joined Chelsea from Athletic Bilbao for £72 million ($91m) in August.
He has enjoyed an encouraging start to life at Stamford Bridge, keeping two clean sheets in the Blues' four Premier League wins to date this season.
Kepa insists his price tag has not added any extra pressure and is pleased to have taken a "gamble" by moving to London.
"It's the price it is because the market is like that, too," he said. "Higher and higher fees are being paid and I see it as a consequence of the market.
"I'm getting used to my new life: a new city, new team... but it's been positive because when things start well on the pitch, it makes everything easier.
"I have felt valued. In the last few years, a lot of Spaniards have done important things here and that's good for those of us to arrive most recently.
"It was an important gamble and I'm happy to take this step. I want to enjoy it."