1-Ethyl-3-methylimidazolium [EMIM], 1-ethylpyridinium [EPY], 1-ethyl-1-methylpyrrolidinium [EPYRO], 4-ethyl-4-methylmorpholium [EMMOK, 1-ethyl-1-methylpiperidinium [EMPIP], and 1,2,4-trimethylpyrazolium [TMPYZO] based cations along with 25 anions have been investigated as possible solvents for the simultaneous hydrodesulfurization (HDS) and hydrodenitrification (FIDN) of diesel oil at T = 298.15 K The infinite dilution activity coefficient (IDAC) of thiophene (TS), benzothiophene (BTS), dibenzothiophene (DBTS), pyrrole (PYR), indole (IND), indoline (INDI), carbazole (CAR), benzocarbazole (BCAR), pyridine (PY), quinoline (QU), and benzoquinoline (BQU) was predicted via the quantum chemical based COSMO-RS (COnductor like Screening MOdel for Real Solvents) model. Subsequently, the selectivity and capacity at infinite dilution were used as indicators for the possible screening of ionic liquids (ILs). [EMMOR], [EMPYRO], and [EMPIP] based cations gave lesser activity coefficient values at infinite dilution as compared to [EMIM], [EPY], and [TMPYZO] based cations. It was noted that [DAV], [BTA], [OcSu], and [MSACN] anions, having a different electronegative atom such as N (nitrogen), O (oxygen), and S (sulfur), respectively, play a significant role in increasing the selectivity. High activity coefficients at infinite dilution values were observed for basic nitrogen compounds as compared to the nonbasic nitrogen compounds irrespective of the cation and anion. Evidently, [EMMOR] and [EPYRO] gave higher solvent capacity values at infinite dilution irrespective of the aromatic nitrogen and sulfur compounds.