The localization of the repeating fast radio burst (FRB), FRB 121102, suggests that it is associated with a persistent radio-luminous compact source in the FRB host galaxy. Using the FIRST radio catalog, I present a search for luminous persistent sources in nearby galaxies, with radio luminosities >10% of the FRB 121102 persistent source luminosity. The galaxy sample contains about 30% of the total galaxy g-band luminosity within <108 Mpc, in a footprint of 10,600 deg^2. After rejecting sources likely due to active galactic nuclei activity or background sources, I remain with 11 candidates that are presumably associated with galactic disks or star formation regions. At least some of these candidates are likely to be due to chance alignment. In addition, I find 85 sources within 1 of galactic nuclei. Assuming the radio persistent sources are not related to galactic nuclei and that they follow the galaxy g-band light, the 11 sources imply a 95% confidence upper limit on the space density of luminous persistent sources of <5x10^-5 Mpc^-3, and that at any given time only a small fraction of galaxies host a radio luminous persistent source (<10^-3 L_*^-1). Assuming persistent sources life time of 100 yr, this implies a birth rate of <5x10^-7 yr^-1 Mpc^-3. Given the FRB volumetric rate, and assuming that all FRBs repeat and are associated with persistent radio sources, this sets a lower limit on the rate of FRB events per persistent source of >0.8 yr^-1. I argue that these 11 candidates are good targets for FRB searches and I estimate the FRB event rate from these candidates.
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