Identifying design problems is a crucial step for creating plausible solutions, but it is challenging for design novices due to their limited knowledge and experience. Questioning is a promising skill that enables students to independently identify design problems without being passive or relying on instructors. This study explores role-playing interactions with Large Language Model (LLM)-powered Conversational Agents (CAs) to foster the questioning skills of novice design students. We proposed an LLM-powered CA prototype and conducted a preliminary study with 16 novice design students engaged in a real-world design class to observe the interactions between students and the LLM-powered CAs. Our findings indicate that while the CAs stimulated questioning and reduced pressure to ask questions, it also inadvertently led to over-reliance on LLM responses. We proposed design considerations and future works for LLM-powered CA to foster questioning skills.