The solvation and solubilization of selected anesthetic active pharmaceutical ingredients (bupivacaine, prilocaine, and procaine) in arginine-based deep eutectic solvents are studied using a theoretical approach considering quantum chemistry and classical molecular dynamics. The intermolecular forces between the anesthetics and the solvent are characterized, with particular attention to hydrogen bonding, in terms of strength, topological properties, interaction mechanism, structuring, and dynamic properties of solvation shells. The reported results show the nanoscopic properties that confirm these solvents as suitable materials for anesthetics drug delivery in the liquid phase.