In this work, a study on the selective solvent extraction (SX) of molybdenum (Mo) and rhenium (Re) from a synthetic pregnant leach solution (PLS) has been carried out using nine different hydrophobic eutectic solvents (HES). Experiments were carried out using pure HES to evaluate the selective extraction and the subsequent stripping of these metal ions; then, the best HES was dissolved in kerosene to study the SX stoichiometry. Results indicated that only TOPO-based and N8881-Cl-based HES did not form emulsions, third phases or precipitates. These HES achieved a selective extraction because these obtained almost a 100% extraction towards Mo and Re from the PLS and very low extractions for Copper (Cu) and Iron (Fe) in one equilibrium stage. The stripping experiments showed that 95% of Mo and 22% of Re were stripped out from the loaded TOPO-based HDES, respectively, opening the possibility for the selective stripping of the metal species for further purification. Finally, the extraction stoichiometry was proposed based on an experimental slope analysis and the measurement of cations and anions transferred into the aqueous phase in which HES acts as a neutral extractant in the complexation of the Mo and Re salts. These promising results suggest that HES could be attractive for more sustainable mining industry.