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Separation of aromatics from aliphatics is a challenging process because of the close range of their boiling points and the formation of several combinations of azeotropes. Until now, no feasible separation process is available for aromatic concentrations below 20 wt%. In this work, we have investigated the possibility of using a selected deep eutectic solvent (DES) for the liquid–liquid extraction of benzene, toluene, ethylbenzene and m-xylene (BTEX) aromatics. The DES used in this work was synthesized by combining tetrabutylammonium salt and sulfolane. Equilibrium data for the ternary system consisting of BTEX aromatics, n-octane and DES were measured at 25 °C and atmospheric pressure. The results showed that the used DESs have comparable distribution ratios and selectivities to those of commercial solvents. In all tested systems, sulfolane was not present in the hydrocarbon layer. It was also found that the selectivity decreases with decreasing polarity of the aromatic compound. The Non-Random Two Liquid (NRTL) model was successfully used to correlate the experimental tie-lines and to calculate the phase compositions of the ternary systems. In addition, the performance of COSMO-RS to predict the ternary tie-lines for the studied systems was evaluated and the σ-profiles were used to explain the interaction between the DES and the aromatic compounds.