Students' ability to ask curious questions is a crucial skill that improves their learning processes. To train this skill, previous research has used a conversational agent that propose specific cues to prompt children's curiosity during learning. Despite showing pedagogical efficiency, this method is still limited since it relies on generating the said prompts by hand for each educational resource, which can be a very long and costly process. In this context, we leverage the advances in the natural language processing field and explore using a large language model (GPT-3) to automate the generation of this agent's curiosity-prompting cues to help children ask more and deeper questions. We then used this study to investigate a different curiosity-prompting behavior for the agent. The study was conducted with 75 students aged between 9 and 10. They either interacted with a hand-crafted conversational agent that proposes "closed" manually-extracted cues leading to predefined questions, a GPT-3-driven one that proposes the same type of cues, or a GPT-3-driven one that proposes "open" cues that can lead to several possible questions. Results showed a similar question-asking performance between children who had the two "closed" agents, but a significantly better one for participants with the "open" agent. Our first results suggest the validity of using GPT-3 to facilitate the implementation of curiosity-stimulating learning technologies. In a second step, we also show that GPT-3 can be efficient in proposing the relevant open cues that leave children with more autonomy to express their curiosity.