Human-Robot Collaboration (HRC) aims to create environments where robots can understand workspace dynamics and actively assist humans in operations, with the human intention recognition being fundamental to efficient and safe task fulfillment. Language-based control and communication is a natural and convenient way to convey human intentions. However, traditional language models require instructions to be articulated following a rigid, predefined syntax, which can be unnatural, inefficient, and prone to errors. This paper investigates the reasoning abilities that emerged from the recent advancement of Large Language Models (LLMs) to overcome these limitations, allowing for human instructions to be used to enhance human-robot communication. For this purpose, a generic GPT 3.5 model has been fine-tuned to interpret and translate varied human instructions into essential attributes, such as task relevancy and tools and/or parts required for the task. These attributes are then fused with perceived on-going robot action to generate a sequence of relevant actions. The developed technique is evaluated in a case study where robots initially misinterpreted human actions and picked up wrong tools and parts for assembly. It is shown that the fine-tuned LLM can effectively identify corrective actions across a diverse range of instructional human inputs, thereby enhancing the robustness of human-robot collaborative assembly for smart manufacturing.