Replacing synthetic surfactants by natural alternatives when formulating nanoemulsions has gained attention as a sustainable approach. In this context, nanoemulsions based on sweet almond oil and stabilized by saponin from Quillaja bark with glycerol as cosurfactant were prepared by the high-pressure homogenization method. The effects of oil/water (O/W) ratio, total surfactant amount, and saponin/glycerol ratio on their stability were analyzed. The formation and stabilization of the oil-in-water nanoemulsions were analyzed through the evaluation of stability over time, pH, zeta potential, and particle size distribution analysis. Moreover, a design of experiments was performed to assess the most suitable composition based on particle size and stability parameters. The prepared nanoemulsions are, in general, highly stable over time, showing zeta potential values lower than −40 mV, a slight acid behavior due to the character of the components, and particle size (in volume) in the range of 1.1 to 4.3 µm. Response surface methodology revealed that formulations using an O/W ratio of 10/90 and 1.5 wt% surfactant resulted in lower particle sizes and zeta potential, presenting higher stability. The use of glycerol did not positively affect the formulations, which reinforces the suitability of preparing highly stable nanoemulsions based on natural surfactants such as saponins.