Clinical trials are a critical process in the medical field for introducing new treatments and innovations. However, cohort selection for clinical trials is a time-consuming process that often requires manual review of patient text records for specific keywords. Though there have been studies on standardizing the information across the various platforms, Natural Language Processing (NLP) tools remain crucial for spotting eligibility criteria in textual reports. Recently, pre-trained large language models (LLMs) have gained popularity for various NLP tasks due to their ability to acquire a nuanced understanding of text. In this paper, we study the performance of large language models on clinical trial cohort selection and leverage the n2c2 challenges to benchmark their performance. Our results are promising with regard to the incorporation of LLMs for simple cohort selection tasks, but also highlight the difficulties encountered by these models as soon as fine-grained knowledge and reasoning are required.