Multilingual large language models have been increasingly popular for their proficiency in comprehending and generating text across various languages. Previous research has shown that the presence of stereotypes and biases in monolingual large language models can be attributed to the nature of their training data, which is collected from humans and reflects societal biases. Multilingual language models undergo the same training procedure as monolingual ones, albeit with training data sourced from various languages. This raises the question: do stereotypes present in one social context leak across languages within the model? In our work, we first define the term ``stereotype leakage'' and propose a framework for its measurement. With this framework, we investigate how stereotypical associations leak across four languages: English, Russian, Chinese, and Hindi. To quantify the stereotype leakage, we employ an approach from social psychology, measuring stereotypes via group-trait associations. We evaluate human stereotypes and stereotypical associations manifested in multilingual large language models such as mBERT, mT5, and ChatGPT. Our findings show a noticeable leakage of positive, negative, and non-polar associations across all languages. Notably, Hindi within multilingual models appears to be the most susceptible to influence from other languages, while Chinese is the least. Additionally, ChatGPT exhibits a better alignment with human scores than other models.