Industrially, deep dearomatization of oil fuels is achieved via catalytic hydrodearomatization (HDA). However, this process suffers from several drawbacks. The most pronounced disadvantages are the intensive energy consumption and the low efficiency toward some aromatic species. With the aim of lowering energy consumption as well as improving the removal efficiency of this process, selective liquid-liquid extraction was proposed in this work. A phosphonium-based deep eutectic solvent (DES) composed of methyltriphenylphosphonium bromide (MTPPBr) and triethylene glycol (TEG) in a molar ratio equal to 1:4 (MTPPBr/TEG) was selected for this investigation. The DES was characterized by its water content, density, viscosity, and degradation temperature. Toluene, thiophene, and quinoline were selected to represent the aromatic species in the oil. However, the oil fuel was represented by n-heptane. Next, the solubility of toluene, thiophene, quinoline, and n-heptane in the pure TEG and MTPPBr/TEG was measured at 298.2 K and 1.01 bar. To assess the selectivities and the solute distribution coefficients of the DES for each compound, liquid-liquid equilibrium (LLE) data for the systems {toluene + n-heptane + MTPPBr/TEG}, {thiophene + n-heptane + MTPPBr/TEG}, and {quinoline + n-heptane + MTPPBr/TEG} were reported at 298.2 K and 1.01 bar. Afterward, a parametric study on an arbitrary oil model of {20% toluene + 2% thiophene + 2% quinoline + 76% n-heptane} was conducted by first testing the single-stage liquid-liquid extraction efficiency for each impurity "toluene, thiophene, and quinoline" at 298.2 K and 1.01 bar. Then, the effects of various operating parameters including the extraction temperature, the solvent-to-feed ratio (S/F), and the initial concentration of the impurity were investigated. Moreover, the number of extraction stages was estimated. Finally, the effect of the repetitive use of DES as well as the possibility of DES regeneration was studied.