The major goal of this work was to study the potential of natural deep eutectic systems (NADES) as new media for ocular formulations. In formulating eye drops, it is important to increase the retention time of the drug on the surface of eye; hence, due to their high viscosity, NADES may be interesting candidates for formulation. Different systems composed of combinations of sugars, polyols, amino acids, and choline derivatives were prepared and then characterized in terms of rheological and physicochemical properties. Our results showed that 5–10% (w/v) aqueous solutions of NADES have a good profile in terms of viscosity (0.8 to 1.2 mPa.s), osmolarity (412 to 1883 mOsmol), and pH (7.4) for their incorporation of ocular drops. Additionally, contact angle and refractive index were determined. Acetazolamide (ACZ), a highly insoluble drug used to treat glaucoma, was used as proof-of-concept. Herein, we show that NADES can increase the solubility of ACZ in aqueous solutions by at least up to 3 times, making it useful for the formulation of ACZ into ocular drops and thereby enabling more efficient treatment. The cytotoxicity assays demonstrated that NADES are biocompatible up to 5% (w/v) in aqueous media, promoting cell viability (above 80%) when compared to the control after 24 h incubation in ARPE-19 cells. Furthermore, when ACZ is dissolved in aqueous solutions of NADES, the cytotoxicity is not affected in this range of concentrations. Although further studies are necessary to design an optimal formulation incorporating NADES, this study shows that these eutectics can be powerful tools in the formulation of ocular drugs.