Modern computing systems exhibit increasing heterogeneity and often require runtime self-management and adaptation to cope with their structural and operational complexity, as well as changes in their environment and requirements. Self-Adaptive Software Systems (SASS) represent a class of context-aware and autonomous systems designed to manage such complexity. However, designing such systems remains challenging due to their complexity, runtime variability, and the continuous need to ensure functional and quality requirements. Large Language Models (LLMs) and Generative AI (Gen AI) offer promising capabilities, yet their use in the architectural design of SASS remains poorly understood. To that end, this study reports a work in progress systematic review. The review findings reveal that the use of LLMs and other Gen AI approaches for the architectural design of SASS remains nascent, with only four relevant studies identified. Across these studies, LLMs act as augmentative reasoning components, concentrated in the monitoring, analysis, planning, and knowledge phases of the MAPE-K loop and are only partially present in execution. Characteristics such as hybrid architectures, multi-agent reasoning, and retrieval-augmented grounding recur across the reviewed studies; however, given the small and heterogeneous evidence base, these are best viewed as preliminary observations rather than established trends, and trustworthiness and runtime assurance remain underexplored.  As a work in progress, this paper contributes an initial characterization of LLM-supported design in self-adaptive systems, outlines research directions, and aims to stimulate discussion within the community on advancing LLM-supported architectural design for self-adaptive and autonomous software systems.