The German goalkeeper, 24, has played second-fiddle to Claudio Bravo in the league for Barca since joining the Catalans in 2014, making just four La Liga starts in two seasons.
Rumours suggested that he could seek a move away, but Ter Stegen insists that he is "very happy" at Camp Nou.
"I'm very happy here and I want to stay here, with the life I have," the Liverpool Echo quotes Ter Stegen as saying. "It's a lovely place to live.
"You can never relax and you always have to give everything. Both myself and Claudio and Jordi [Masip] want to play and we work week after week to do so.
"I think that this idea is good for the team, too, because we're always ready."
Ter Stegen still has three years left on his Barca contract.