Most nonsteroidal anti-inflammatory drugs (NSAIDs) present poor aqueous solubility, impairing their efficiency in physiological media. In this context, Low Transition Temperature Mixtures (LTTMs) are a promising platform to overcome drugs’ poor solubility, forming therapeutic liquid formulations. In this work, the LTTMs of citric acid:L-arginine:water (C:A:W) and glycerol:sorbitol (G:S) were studied in terms of their features and assessed in terms of their ability to increase the solubility of six NSAIDs in physiological media. The physicochemical properties of LTTMs were characterized by state-of-art techniques commonly used for these systems. The cytotoxicity of G:S was also evaluated in L929 mouse fibroblasts and the viscosity, polarity, and pH properties of the studied mixtures were related to the solubility of NSAIDs. The pH and polarity were the parameters that most influenced the drugs’ solubility. Ibuprofen, naproxen, ketoprofen, indomethacin, and flurbiprofen did not present any solubility improvement in the formulations tested. However, concentrated mixtures of C:A:W or G:S in the physiologic-mimicked media (PBS) rendered a celecoxib solubility 4 and 5 times higher than PBS, respectively. These therapeutic liquid formulations of celecoxib in C:A:W or G:S can be a promising tool to increase celecoxib’s therapeutic efficiency in local applications.