The highly-rated 21-year-old stopper's current deal runs until the summer of 2015, but the Germans have been unable to convince him to commit for longer, making a cash-in either this month or in the summer the likely scenario.
Moenchengladbach sporting director Max Eberl announced the news on Monday and added even more fuel to the speculation that Ter Stegen will indeed head to Liga giants Barcelona, who have long been admirers of the goalkeeper.
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."
Barcelona are looking for a replacement for Victor Valdes, who will leave the club after almost two decades on their books at the end of the season.
Barca vice-president Josep Bartomeu said in November while confirming their quest for a replacement that they only require "one goalkeeper and not two".
This could spell the end of links between Napoli's Liverpool-loaned custodian Pepe Reina and the Camp Nou.
Moenchengladbach are enjoying a fine run in the Bundesliga, with Ter Stegen's six clean sheets helping them reach third in the table.