Supermassive black hole binaries (SMBHBs) should form frequently in galactic nuclei as a result of galaxy mergers. At subparsec separations, binaries become strong sources of low-frequency gravitational waves (GWs), targeted by Pulsar Timing Arrays. We used recent upper limits on continuous GWs from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11yr data set to place constraints on putative SMBHBs in nearby massive galaxies. We compiled a comprehensive catalog of ~44000 galaxies in the local universe (up to redshift ~0.05) and populated them with hypothetical binaries, assuming that the total mass of the binary is equal to the SMBH mass derived from global scaling relations. Assuming circular equal-mass binaries emitting at NANOGrav's most sensitive frequency of 8nHz, we found that 216 galaxies are within NANOGrav's sensitivity volume. We ranked the potential SMBHBs based on GW detectability by calculating the total signal-to-noise ratio such binaries would induce within the NANOGrav array. We placed constraints on the chirp mass and mass ratio of the 216 hypothetical binaries. For 19 galaxies, only very unequal-mass binaries are allowed, with the mass of the secondary less than 10% that of the primary, roughly comparable to constraints on an SMBHB in the Milky Way. However, we demonstrated that the (typically large) uncertainties in the mass measurements can weaken the upper limits on the chirp mass. Additionally, we were able to exclude binaries delivered by major mergers (mass ratio of at least 1/4) for several of these galaxies. We also derived the first limit on the density of binaries delivered by major mergers purely based on GW data.