Generative artificial intelligence (GenAI), exemplified by ChatGPT, Midjourney, and other state-of-the-art large language models and diffusion models, holds significant potential for transforming education and enhancing human productivity. While the prevalence of GenAI in education has motivated numerous research initiatives, integrating these technologies within the learning analytics (LA) cycle and their implications for practical interventions remain underexplored. This paper delves into the prospective opportunities and challenges GenAI poses for advancing LA. We present a concise overview of the current GenAI landscape and contextualise its potential roles within Clow's generic framework of the LA cycle. We posit that GenAI can play pivotal roles in analysing unstructured data, generating synthetic learner data, enriching multimodal learner interactions, advancing interactive and explanatory analytics, and facilitating personalisation and adaptive interventions. As the lines blur between learners and GenAI tools, a renewed understanding of learners is needed. Future research can delve deep into frameworks and methodologies that advocate for human-AI collaboration. The LA community can play a pivotal role in capturing data about human and AI contributions and exploring how they can collaborate most effectively. As LA advances, it is essential to consider the pedagogical implications and broader socioeconomic impact of GenAI for ensuring an inclusive future.