We present an imaging survey that searches for the stellar counterparts of recently discovered ultra-compact high-velocity H i clouds (UCHVC). It has been proposed that these clouds are candidate mini-haloes in the Local Group and its surroundings within a distance range of 0.25-2.0 Mpc. Using the Large Binocular Telescope we obtained wide-field (≃ 23' × 23') g- and r-band images of the twenty-five most promising and most compact clouds amongst the fifty-nine that have been identified. Careful visual inspection of all the images does not reveal any stellar counterpart that even slightly resembles Leo P, 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 in our images. The point source photometry in the central 17.3' × 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 Leo P field, in which the dwarf galaxy is detected at a >30σ-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 show that our survey would have detected any dwarf galaxy dominated by an old stellar population, with an integrated absolute magnitude of MV ≤ - 8.0 and a half-light radius of rh ≤ 300 pc that lies within 1.5 Mpc of us, thereby confirming that it is unlikely that the observed UCHVCs are associated with the stellar counterparts typical of known Local Group dwarf galaxies. Based on data acquired using the Large Binocular Telescope (LBT). The LBT is an international collaboration amongst institutions in the United States, Italy, and Germany. LBT Corporation partners are The University of Arizona on behalf of the Arizona university system; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State University; and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota, and University of Virginia.Appendices are available in electronic form at http://www.aanda.org