The 21-year-old has been widely linked with a move away from the Bundesliga outfit, with Barcelona reported to be leading the chase for his signature as they seek to replace Victor Valdes.
Ter Stegen has a contract at Borussia Park until 2015, but attempts to get him to sign a new deal have been rejected, according to sporting director Max Eberl.
The club announced the news on their official twitter account, posting: "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 doesn't surprise us. I assume he'll join the club he has been linked to."
Ter Stegen has kept six clean sheets for Monchengladbach this season, helping them climb to third in the Bundesliga.
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