Large language models (LLMs) are capable of efficiently understanding natural language by processing large volumes of text data. Natural language is also used in process descriptions, thus LLMs appear to be a suitable candidate to significantly improve business process modeling. Although plenty of third-party LLMs exist, they raise the risk of privacy disclosure, untrustworthiness, and generalizability of the results. This paper proposes a pipeline to use a local and fine-tuned LLM that expects a textual process description as input and finally generates a visual process tree representation. We instantiate our pipeline with Llama3 8B and fine-tune the LLM with a training set of 120 self-generated examples. Initial evaluation results of our LLM-based approach for automated business process modeling promise usefulness of the approach in terms of process model quality while preserving data privacy.