Effective physician-patient communications in pre-diagnostic environments, and most specifically in complex and sensitive medical areas such as infertility, are critical but consume a lot of time and, therefore, cause clinic workflows to become inefficient. Recent advancements in Large Language Models (LLMs) offer a potential solution for automating conversational medical history-taking and improving diagnostic accuracy. This study evaluates the feasibility and performance of LLMs in those tasks for infertility cases. An AI-driven conversational system was developed to simulate physician-patient interactions with ChatGPT-4o and ChatGPT-4o-mini. A total of 70 real-world infertility cases were processed, generating 420 diagnostic histories. Model performance was assessed using F1 score, Differential Diagnosis (DDs) Accuracy, and Accuracy of Infertility Type Judgment (ITJ). ChatGPT-4o-mini outperformed ChatGPT-4o in information extraction accuracy (F1 score: 0.9258 vs. 0.9029, p = 0.045, d = 0.244) and demonstrated higher completeness in medical history-taking (97.58% vs. 77.11%), suggesting that ChatGPT-4o-mini is more effective in extracting detailed patient information, which is critical for improving diagnostic accuracy. In contrast, ChatGPT-4o performed slightly better in differential diagnosis accuracy (2.0524 vs. 2.0048, p > 0.05). ITJ accuracy was higher in ChatGPT-4o-mini (0.6476 vs. 0.5905) but with lower consistency (Cronbach's $α$ = 0.562), suggesting variability in classification reliability. Both models demonstrated strong feasibility in automating infertility history-taking, with ChatGPT-4o-mini excelling in completeness and extraction accuracy. In future studies, expert validation for accuracy and dependability in a clinical setting, AI model fine-tuning, and larger datasets with a mix of cases of infertility have to be prioritized.