The 21-year-old has been widely linked with a move away from the Bundesliga outfit, with Barcelona's vice-president Josep Bartomeu admitting their interest in the shot-stopper in November as they seek a replacement for the outgoing Victor Valdes.
Ter Stegen has a contract at Borussia Park until 2015, but the club have announced that attempts to tie him down by agreeing a new deal have been rejected.
Sporting director Max Eberl said: "Ter Stegen will leave Borussia. Marc has informed us that will not accept our offer of a new contract.
"Marc's decision not to renew does not surprise us. I assume he'll join the club he has been linked to."
Ter Stegen has kept six clean sheets for Gladbach this season, helping them climb to third in the Bundesliga.
And he insists he is still committed to the club despite rejecting the new deal.
"I do not want to comment on the state of play. And I do not want to talk about the 'Why" and the reasons I had in public," he told reports after training on Monday.
"I thought about this for a long time. I always said I would decide during the winter break and that is what I did. I will continue to play full throttle for this club."