The first meeting of the Multistakeholder Advisory Body on AI should embrace a long-term perspective based on the positive and negative effects associated with Artificial Intelligence (AI). Therefore, while taking the competences and objectives of the United Nations as basis and starting point for how to design the AI governance system at UN level, current governance and regulatory models at UN level can serve as a model but should not limit the choices for the future AI governance, considering ongoing developments across the world to regulate AI. The paper will outline some potential governance models existing at international level and describe their advantages and drawbacks (I.) The paper finally argues that any chosen governance structure of an AI agency or advisory body will ideally embrace the human rights-based approach, the SDGs and involve existing UN bodies with their respective competencies and know-how. In order to create an efficient UN agency, the choice of the model and its internal procedural rules are of great importance in order to ensure a good functioning of the body and the fulfillment of its mandate (II.).