The last decade witnessed an increasing interest in axions and axion-like particles with many theoretical works published and many new experimental proposals that started a real race towards their discovery. This paper is the Conceptual Design Report of the KLASH (KLoe magnet for Axion SearcH) experiment at the Laboratori Nazionali di Frascati (LNF). The idea of this experiment has been stimulated by the availability of the large volume superconducting magnet, with a moderate magnetic field of 0.6 T, used in the KLOE detector at the DAFNE collider. The main conclusion we draw from this report is the possibility to build and put in operation at LNF in 2-3 years a large haloscope with the sensitivity to KSVZ axions in the low mass range between 0.2 and 1 $mu$eV, complementary to that of other experiments. Timeline and cost are competitive with respect to other proposals in the same mass region thanks to the availability of most of the infrastructure, in particular the superconducting magnet and the cryogenics plant.
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