Using surface X-ray diffraction we have studied the atomic structure of ultrathin silver films deposited in the one monolayer thickness-regime on the (0001) surface of the Topological Insulator Bi2Se3. Depending on the preparation of the substrate surface, different interface structures are formed. For sputter-annealed single crystalline Bi₂Se₃ (0001) silver atoms substitute bismuth atoms within the first quintuple layer and simultaneously reside in surface hollow sites. When silver is deposited on a substrate grown by molecular beam epitaxy and which was only annealed prior to silver deposition, only adsorption in surface hollow sites is observed. Neither intercalation into the van der Waals gap nor its vertical expansion is observed in any case. An expansion induced appearance of surface states can be excluded.