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 <108Mpc, in a footprint of 10600deg^2^. After rejecting sources likely due to active galactic nuclei activity or background sources, I am left 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 that 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 a persistent source lifetime of 100 years, 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 >~0.8yr^-1^. I argue that these 11 candidates are good targets for FRB searches and I estimate the FRB event rate from these candidates.