  We present an imaging survey aimed at searching for the stellar counterparts
of recently discovered ultra-compact high-velocity HI clouds (UCHVC). Adams et
al. (2013) proposed these clouds to be candidate mini-haloes in the Local Group
and/or its surroundings, within a distance range of 0.25-2.0 Mpc. Using the
Large Binocular Telescope we obtain wide-field (~ 23' X 23') g- and r-band
images of the twenty-five most promising and most compact clouds among the
fifty-nine identified by Adams et al. Careful visual inspection of all the
images does not reveal any stellar counterpart even slightly resembling LeoP,
the only local dwarf galaxy that was found as a counterpart to a previously
detected high velocity cloud. Only a possible distant (D>3.0 Mpc) counterpart
to HVC274.68+74.70-123 has been identified on our images. The point source
photometry in the central 17.3' X 7.7' chips reaches r<= 26.5, and is expected
to contain most of the stellar counterparts to the UCHVCs. However, no obvious
stellar over-density is detected in any of our fields, in marked contrast to
our comparison LeoP field in which the dwarf galaxy is detected at a >30 sigma
significance level. Only HVC352.45+59.06+263 may be associated with a weak
over-density, whose nature cannot be ascertained with our data. Sensitivity
tests shows that our survey would have detected any dwarf galaxy dominated by
an old stellar population, with an integrated absolute magnitude M_V<= -8.0, a
half-light radius r_h<= 300 pc, and lying within 1.5 Mpc from us, thereby
confirming that it is unlikely that the observed UCHVCs are associated with
stellar counterparts typical of known Local Group dwarf galaxies.
