The X-ray source CXO J133815.6+043255 has counterparts in the UV, optical, and radio bands. Based on the multi-band investigations, it has been recently proposed by Kim et al. (2015) as a rarely-seen off-nucleus ultraluminous X-ray (ULX) source with a black hole mass of ≥ 10 4 M ⊙ in the nearby Seyfert galaxy NGC 5252. To explore its radio properties at very high angular resolution, we performed very longbaseline interferometry (VLBI) observations with the European VLBI Network (EVN) at 1.7 GHz. We find that the radio counterpart is remarkably compact among the known ULXs. It does not show a resolved structure with a resolution of a few milliarcsecond (mas), and the total recovered flux density is comparable to that measured in earlier sub-arcsecond-resolution images. The compact radio structure, the relatively flat spectrum, and the high radio luminosity are consistent with a weakly accreting supermassive black hole in a low-luminosity active galactic nucleus. The nucleus of NGC 5252 itself has similar radio properties. We argue that the system represents a relatively rare pair of active galactic nuclei, where both components emit in the radio.