The German goalkeeper joined Barca from Borussia Monchengladbach in 2014 and has been a first-team regular at Camp Nou for the past four seasons.
Both Ter Stegen and Barcelona are keen to extend his contract, though, with negotiations having already started before the coronavirus pandemic struck.
"It's not possible that I'll leave this summer," he told Kicker.
"There were some initial meetings between my agent and the club [regarding a renewal]. Then the virus got in the way and it wasn't the moment to talk about a contract.
"At a time when many people were concerned for their lives, we decided to postpone it.
"I feel good in Barcelona, also because my family feel good."
Ter Stegen has made 224 appearances for Barca in all competitions, 34 of those coming this season. body check tags ::