Searches for Earth-skimming neutrinos using volcanoes have not yet been achieved, but it is a promising technique for the detection of neutrinos above 1 PeV. The HAWC observatory is located in the vicinity of the highest mountain in Mexico, the Pico de Orizaba volcano, which shields the detector from quasi-horizontal very high-energy (VHE) muons. The large amount of shielding, up to 8 km of rock, enables the suppression of the large VHE muon background and makes neutrino detection possible. In this work we present the first steps towards the implementation of the Earth-skimming technique for the indirect measurement of tau neutrinos with HAWC. The results include the description of the charged lepton tracking reconstruction algorithm developed for this study and the initial analysis of the background of VHE muons using half a year of data.