The growing demand for healthier lipid alternatives has driven interest in oleogels as promising substitutes for the conventional saturated and trans fats in foods systems. In this context, this study explores the formulation and characterization of oleogels based on avocado oil (Persea americana var. Lorena) and monoglycerides, as an alternative to conventional saturated fats. Hydraulic compression was used to extract the oil, and the formulation was optimized using a Box–Behnken experimental design, evaluating the effects of temperature (70–90 °C), monoglyceride concentration (4–8%), and heating time (15–45 min) on oil retention capacity (ORC) and firmness. Results showed that temperature and concentration significantly influenced ORC and firmness, while heating time had no relevant effect. The optimal formulation achieved 85.95% ORC, 1.09 N firmness, and superior oxidative stability (41.71 h vs. 10.80 h in pure oil, Rancimat test). The obtained oleogel exhibited good mechanical and thermal properties, with an elastic-dominant rheological profile and higher oxidation resistance compared to unmodified avocado oil. These findings indicate that the avocado oleogels structured with monoglycerides have potential applications in the food and cosmetic industries, although further improvements in structural stability are recommended to broaden their range of applications.