The purpose of our study was to select the most effective ionic liquid extraction solvents for dysprosium (III) fluoride using a theoretical approach. Conductor-like Screening Model for Real Solvents (COSMO-RS), based on quantum chemistry and the statistical thermodynamics of predefined DyF3-ionic liquid systems, was applied to reach the target. Chemical potentials of the salt were predicted in 4,400 different ionic liquids. On the base of these predictions set of ionic liquids' ions, manifesting significant decrease of the chemical potentials, were selected. Considering the calculated physicochemical properties (hydrophobicity, viscosity) of the ionic liquids containing these specific ions, the most effective extraction solvents for liquid-liquid extraction of DyF3 were proposed. The obtained results indicate that the COSMO-RS approach can be applied to quickly screen the affinity of any rare earth element for a large number of ionic liquid systems, before extensive experimental tests. © 2015 AIP Publishing LLC.