You can't make a transformer-based language model "have" curiosity.
Real curiosity is an innate trait in intelligent animals that promotes learning and exploration by increasing focus and stick-to-it-ness when the situation is interesting/unexplored (i.e. not well predicted - surprising).
An LLM could be trained to fake curiosity in same way that ELIZA did ("Tell me more about your fear of prison showers"), but fundamentally it deals in words and statistics, not facts and memories, so any poorly-predicted surprise signal will be surface level such as "that was an unusual word pattern" or "you haven't mentioned that before in the input context".
Even if fake curiosity ("interest") makes the model seem more conversationally engaging, maybe helps exploration by prompting the use to delve deeper into a subject, it's not going to help learning since LLMs are pre-trained and cannot learn by experience (except ephemerally within context).