This paper explores the integration of Artificial Intelligence (AI) in the design of interactive experiences for Cultural Heritage (CH). Previous studies indeed either miss to represent the specificity of the CH or mention possible tools without making a clear reference to a structured Interaction Design (IxD) workflow. The study also attempts to overcome one of the major limitations of traditional literature review, which may fail to capture proprietary tools whose release is rarely accompanied by academic publications. Besides the analysis of previous research, the study proposes a possible workflow for IxD in CH, subdivided into phases and tasks: for each of them, this paper proposes possible AI-based tools that can support the activity of designers, curators, and CH professionals. The review concludes with a final section outlining future paths for research and development in this domain.