Poor water solubility represents a serious issue for drug formulation and delivery. Cyclodextrins (CDs) and cosolvents are valuable approaches to overcome this issue. Currently, there is a growing interest in deep eutectic solvents (DESs) with high solubilizing ability and low toxicity. Low melting mixtures (LMMs) based on CDs have recently emerged, combining the solubilizing properties of solvents and drug carriers. In this study, we evaluated the solubility of ketoprofen, flurbiprofen and naproxen in two mixtures based on levulinic acid (Lev). The effect of water on the solubilizing potential and viscosity of these mixtures was assessed. Also, the stability of the studied drugs was monitored up to one year. The LMM based on randomly methylated-β-cyclodextrin (RAMEB) showed the highest solubilizing potential (up to 5012-fold the aqueous solubility) compared to the DES based on choline chloride. Formation of RAMEB/drug inclusion complex in the LMM was evidenced by nuclear magnetic resonance spectroscopy (NMR). Adding water (10 wt%) sharply reduced the viscosity of both mixtures while maintaining their high solubilizing ability. Moreover, the studied drugs were stable up to 90% in both mixtures after a year at 25 °C. Such low-viscous mixtures endowed with high solubilizing and stabilizing properties have great potential for pharmaceutical applications.