The Daily Star says the Gladbach keeper, 21, was understood to have signed a pre-contract agreement to join Barca at the end of the season.
However, the La Liga giants haven't stumped up enough cash.
They are still £1.6m short of what Monchengladbach are after and the Gunners could nip in and gatecrash the deal.
Arsenal can sign Ter Stegen for £10.2m.
Gunners boss Arsene Wenger wants a high-class stopper to challenge Wojciech Szczesny for the No.1 shirt.
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