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Abstract We present 1–12 GHz Karl G. Jansky Very Large Array observations of nine off-nuclear persistent radio sources (PRSs) in nearby (z≲ 0.055) dwarf galaxies, along with high-resolution European VLBI Network observations for one of them at 1.7 GHz. We explore the plausibility that these PRSs are associated with fast radio burst (FRB) sources by examining their properties—physical sizes, host-normalized offsets, spectral energy distributions (SEDs), radio luminosities, and light curves—and compare them to those of the PRSs associated with FRB 20121102A and FRB 20190520B, two known active galactic nuclei (AGN), and one likely AGN in our sample with comparable data, as well as other radio transients exhibiting characteristics analogous to FRB-PRSs. We identify a single source in our sample, J1136+2643, as the most promising FRB-PRS, based on its compact physical size and host-normalized offset. We further identify two sources, J0019+1507 and J0909+5655, with physical sizes comparable to FRB-PRSs, but which exhibit large offsets and flat spectral indices potentially indicative of a background AGN origin. We test the viability of neutron star wind nebula and hypernebula models for J1136+2643 and find that the physical size, luminosity, and SED of J1136+2643 are broadly consistent with these models. Finally, we discuss the alternative interpretation that the radio sources are instead powered by accreting massive black holes, and we outline future prospects and follow-up observations for differentiating between these scenarios.