Generative artificial intelligence (GenAI) models have advanced various applications with their ability to generate diverse forms of information, including text, images, audio, video, and 3D models. In visual computing, their primary applications have focused on creating graphic content and enabling data visualization on traditional desktop interfaces, which help automate visual analytics (VA) processes. With the rise of affordable immersive technologies, such as virtual reality (VR), augmented reality (AR), and mixed reality (MR), immersive analytics (IA) has been an emerging field offering unique opportunities for deeper engagement and understanding of complex data in immersive environments (IEs). However, IA system development remains resource-intensive and requires significant expertise, while integrating GenAI capabilities into IA is still under early exploration. Therefore, based on an analysis of recent publications in these fields, this position paper investigates how GenAI can support future IA systems for more effective data exploration with immersive experiences. Specifically, we discuss potential directions and key issues concerning future GenAI-supported IA applications.