Abstract Tectonic tremor has been observed at the roots of many fault systems around the Pacific rim, including convergent and transform plate boundaries. The extent to which deep tremor signals are prevalent along fault systems elsewhere, including the Mediterranean basin, has not yet been documented in detail. A body of evidence suggests that tremor triggered during the surface waves of teleseismic events may commonly occur where ambient tremor during episodic tremor and slip episodes occur, suggesting triggered tremor provides a useful tool to identify regions with ambient tremor. We perform a systematic search of triggered tremor associated with large teleseismic events between 2010 and 2020 at four major fault systems within the central‐eastern Mediterranean basin, namely the Hellenic and Calabrian subduction zones, and the North Anatolian and Kefalonia transform faults. In addition, we search for ambient tremor during a slow slip event in the eastern Sea of Marmara along a secondary branch of the North Anatolian Fault, and two slow slip events beneath western Peloponnese (Hellenic Subduction Zone). We find no unambiguous evidence for deep triggered tremor, nor ambient tremor. The absence of triggered tremor at the Hellenic and Calabrian subduction zones supports an interpretation of less favorable conditions for tremorgenesis in the presence of old and cold slabs. The absence of tremor along the transform faults may be due to an absence of the conditions commonly promoting tremorgenesis in such settings, including high‐fluid pressures and low‐differential stresses between the down‐dip limit of the seismogenic layer and the continental Moho.