The 21-year-old is considered to be one of European football's most promising goalkeepers.
His development has been noted by clubs in Germany and across the continent, with Barca among those to have cast an admiring eye in his direction.
The Catalan giants are in the market for a long-term replacement for Victor Valdes, who has decided against extending his contract at Camp Nou, but Monchengladbach are adamant that they have fielded no requests from Spain.
Director of football Max Eberl told Fohlen-Hautnah: "He's here. Any further comment about it would be too much.
"If the Spaniards like to invent these stories, it's another thing.
"Neither the player nor Borussia Monchengladbach know anything about any interest, a deal or an agreement. We're building something up here, and I think he likes being a part of it."
On reports that Ter Stegen has a release clause in his contract, Eberl added: "His agent said this six times before to newspapers (that there is no clause).
"Now I say it for the seventh time - and I don't want to be asked about it again."