Assortment planning, integral to multiple commercial offerings, is a key problem studied in e-commerce and retail settings. Numerous variants of the problem along with their integration into business solutions have been thoroughly investigated in the existing literature. However, the nuanced complexities of in-store planning and a lack of optimization proficiency among store planners with strong domain expertise remain largely overlooked. These challenges frequently necessitate collaborative efforts with multiple stakeholders which often lead to prolonged decision-making processes and significant delays. To mitigate these challenges and capitalize on the advancements of Large Language Models (LLMs), we propose an interactive assortment planning framework, InteraSSort that augments LLMs with optimization tools to assist store planners in making decisions through interactive conversations. Specifically, we develop a solution featuring a user-friendly interface that enables users to express their optimization objectives as input text prompts to InteraSSort and receive tailored optimized solutions as output. Our framework extends beyond basic functionality by enabling the inclusion of additional constraints through interactive conversation, facilitating precise and highly customized decision-making. Extensive experiments demonstrate the effectiveness of our framework and potential extensions to a broad range of operations management challenges.