Although Large Language Models (LLMs) have shown promising performance in healthcare-related applications, their deployment in the medical domain poses unique challenges of ethical, regulatory, and technical nature. In this study, we employ a systematic participatory approach to investigate the needs and expectations regarding clinical applications of LLMs at Lausanne University Hospital, an academic medical center in Switzerland. Having identified potential LLM use-cases in collaboration with thirty stakeholders, including clinical staff across 11 departments as well nursing and patient representatives, we assess the current feasibility of these use-cases taking into account the regulatory frameworks, data protection regulation, bias, hallucinations, and deployment constraints. This study provides a framework for a participatory approach to identifying institutional needs with respect to introducing advanced technologies into healthcare practice, and a realistic analysis of the technology readiness level of LLMs for medical applications, highlighting the issues that would need to be overcome LLMs in healthcare to be ethical, and regulatory compliant.