Important efforts have been made over the past years to improve the drug acts, which leads to the discovery of novel drug preparations and delivery systems. The selection of suitable green solvents for novel drug discovery and drug delivery depends on a molecular-level understanding of the interaction between drug molecules and the solvents. Deep eutectic solvents (DESs) are already used in sustainable extraction methods of natural products for their very high solvent power, high chemical and thermal stability, non-toxicity, and non-flammable. The thermodynamic investigation provides deep and complete knowledge of interactions and the choice of appropriate and suitable production compounds in pharmaceutical fields. Particularly, the analysis of drugs+DESs in aqueous media is a central issue in many types of research. This research is aimed to determine hesperidin (HES) solubility in water and DES solvents [choline chloride/citric acid (ChCl/CA), choline chloride/oxalic acid (ChCl/OA), choline chloride/malonic acid (ChCl/MA), and choline chloride/lactic acid (ChCl/LA)] at temperature range (298.15–313.15 K). Furthermore, the measured solubility data of HES in studied aqueous DESs solutions was fitted by models of Van’t Hoff–Jouyban–Acree and Modified Apelblat–Jouyban–Acree. Finally, the Hansen solubility parameters as thermodynamic aspect for analyzing the dissolution processes for the four investigated aqueous DESs solutions were estimated.