Social categories and stereotypes embedded in language can introduce data bias into the training of Large Language Models (LLMs). Despite safeguards, these biases often persist in model behavior, potentially leading to representational harm in outputs. While sociolinguistic research provides valuable insights into the formation and spread of stereotypes, NLP approaches for bias evaluation rarely draw on this foundation and often lack objectivity, precision, and interpretability. To fill this gap, we propose a new approach to assess stereotypes by detecting and quantifying the linguistic indication of a stereotype. We derive linguistic indicators from the Social Category and Stereotype Communication (SCSC) framework indicating strong social category formulation and stereotyping in language, and use them to build a categorization scheme. We use in-context learning to instruct LLMs to examine the linguistic properties of a sentence containing stereotypes, providing a basis for a fine-grained stereotype assessment. We develop a scoring function to measure linguistic indicators of stereotypes based on empirical evaluation. Our annotations of stereotyped sentences reveal that these linguistic indicators explain the strength of a stereotype. The models perform well in detecting and classifying linguistic indicators used to denote a category, but sometimes struggle with accurately evaluating the described associations. The use of more few-shot examples significantly improves the performance. Model performance increases with size, as Llama-3.3-70B-Instruct and GPT-4 achieve comparable results that surpass those of Mixtral-8x7B-Instruct, GPT-4-mini and Llama-3.1-8B-Instruct_4bit. Code and annotations can be found in https://github.com/r-goerge/Detecting-Linguistic-Indicators-for-Stereotype-Assessment-with-LLMs.