Supervising a PhD candidate towards acquiring the requisite skills and competencies throughout their PhD journey is a fundamental aspect of PhD supervision. The emergence of various Generative Artificial Intelligence (GenAI) tools, such as ChatGPT, could be a potential paradigm shift for academic design research. Given the context, the consequences of the incorporation of GenAI in the supervision process need to be carefully explored to reap the benefits of such a modified approach in a transparent and ethical manner. This paper presents an exploratory study of PhD supervision activities influenced by GenAI, outlining the affected skills and competencies of PhD supervisors. The study involved conducting 11 semi-structured interviews with PhD supervisors from the engineering design community, which were subjected to a detailed analysis. Preliminary findings are presented, accompanied by a set of recommendations to navigate this emerging interface between GenAI and PhD supervision.