Advances in Large Language Models (LLMs) have triggered an unprecedented surge in innovation, leading to a rapid proliferation of novel applications, such as recommendation systems. In this work, we take advantage of these developments and present our preliminary investigation of the potential of deploying LLMs-based persuasive strategies: polite, authority, emotional engagement, scarcity, and social proof in Social Assistive Robots for healthier snack choices. We carried out the study in two phases: Firstly, using a within-subject design involving N = 124 Italian college students from diverse academic disciplines, we examined the extent to which individuals consider the healthiness of snacks before purchasing and consuming them. Findings from the study suggest that most subjects have good knowledge of what a “healthy snack” is. However, many participants frequently neglect to consider the healthiness of these snacks before purchasing and consuming them. Next, through a between-subjects experiment involving N = 166 college students, we investigate the influence of users’ personality trait tendencies (trust propensity (TP) and compliance awareness (CA)) and the Big Five factors on preferences for the robot’s LLM-driven strategies for eliciting healthier snack choices. Results showed variation in the preference for these strategies relative to subjects’ trait tendencies. Specifically, subjects in the TP and CA groups appraised these strategies differently regarding the impression items: persuasiveness, willingness, and trustworthiness.