  Aims. We aim at finding candidates of potential survivors of high-redshift
compact galaxies in SDSS, as targets for more detailed follow-up observations.
  Methods. From the virial theorem it is expected that for a given mass,
compact galaxies have stellar velocity dispersion higher than the mean due to
their smaller sizes. Therefore velocity dispersion coupled with size (or mass)
is an appropriate method to select relics, independent of the stellar
population properties. Based on these consideration we design a set of criteria
using distribution of early-type galaxies from SDSS on the
log$_{10}$(R$_{0}$)-log$_{10}$($\sigma_{0}$) plane to find the most extreme
objects on it.
  Results. We find 76 galaxies at 0.05 < z < 0.2, which have properties similar
to the typical quiescent galaxies at high redshift. We study how well these
galaxies fit on well-known local universe relations of early-type galaxies such
as the fundamental plane, the red sequence or mass-size relations. As expected
from the selection criteria, the candidates are located in an extreme corner of
mass-size plane. However, they do not extend as deeply into the so-called zone
of exclusion as some of the high-redshift compact galaxies ('red nuggets')
found at high redshift, being a factor 2-3 less massive at a given intrinsic
scale size. Our candidates are systematically offset from scaling relations of
average early-type galaxies, while being in the mass-size range expected for
passive evolution of the red nuggets from their high redshift to the present.
  Conclusions. The 76 selected candidates form a well suited set of objects for
further follow-up observations. We argue that selecting a high velocity
dispersion is the best way to find analogues of compact high redshift galaxies
in the local universe.
