Prompted by recent innovations, artificial intelligence (AI) is increasingly being discussed across the museum sector regarding its implications for institutional roles and practices. However, AI in particular, is an ambiguous term, a ‘black box’ which is capable of containing and reflecting numerous values and ideals (Crawford, 2021). This paper positions discourse around AI as a ‘discursive’ infrastructure, capable of not only embodying ideals but also shaping and justifying certain institutional practices and roles. This paper thematically analyses 115 pieces of grey literature produced and shared by professional governance bodies in the museum sector from 1995–2023, mainly across Canada, the United Kingdom, and the United States. In doing so, it identifies four preliminary themes encompassing shifts in discourse over time which give shape to a contemporary discursive infrastructure. This prompts timely critical reflections of museum professionals and stakeholders on both imagined and overlooked public roles, responsibilities, and practices of the museum in relation to AI.