  We report on a search for host galaxies of a subset of Rotating Radio
Transients (RRATs) that possess a dispersion measure (DM) near or above the
maximum Galactic value in their direction. These RRATs could have an
extragalactic origin and therefore be Fast Radio Bursts (FRBs). The sizes of
related galaxies on the sky at such short distances are comparable to the beam
size of a single-dish telescope (for example, the $7.0'$ radius of the Parkes
beam). Hence the association, if found, could be more definitive as compared to
finding host galaxies for more distant FRBs. We did not find any host galaxy
associated with six RRATs near the maximum Galactic DM. This result is
consistent with the fact that the probability of finding an FRB host galaxy
within this volume is also very small. We propose that future follow-up
observations of such RRATs be carried out in searching for local host galaxies
as well as the sources of FRBs.
