Artificial Intelligence (AI) is expected to be an integral part of next-generation AI-native 6G networks. With the prevalence of AI, researchers have identified numerous use cases of AI in network security. However, there are almost nonexistent studies that analyze the suitability of Large Language Models (LLMs) in network security. To fill this gap, we examine the suitability of LLMs in network security, particularly with the case study of STRIDE threat modeling. We utilize four prompting techniques with five LLMs to perform STRIDE classification of 5G threats. From our evaluation results, we point out key findings and detailed insights along with the explanation of the possible underlying factors influencing the behavior of LLMs in the modeling of certain threats. The numerical results and the insights support the necessity for adjusting and fine-tuning LLMs for network security use cases.