In this paper we present Large Language Model Assisted Retrieval Model Ranking (LARMOR), an effective unsupervised approach that leverages LLMs for selecting which dense retriever to use on a test corpus (target). Dense retriever selection is crucial for many IR applications that rely on using dense retrievers trained on public corpora to encode or search a new, private target corpus. This is because when confronted with domain shift, where the downstream corpora, domains, or tasks of the target corpus differ from the domain/task the dense retriever was trained on, its performance often drops. Furthermore, when the target corpus is unlabeled, e.g., in a zero-shot scenario, the direct evaluation of the model on the target corpus becomes unfeasible. Unsupervised selection of the most effective pre-trained dense retriever becomes then a crucial challenge. Current methods for dense retriever selection are insufficient in handling scenarios with domain shift. Our proposed solution leverages LLMs to generate pseudo-relevant queries, labels and reference lists based on a set of documents sampled from the target corpus. Dense retrievers are then ranked based on their effectiveness on these generated pseudo-relevant signals. Notably, our method is the first approach that relies solely on the target corpus, eliminating the need for both training corpora and test labels. To evaluate the effectiveness of our method, we construct a large pool of state-of-the-art dense retrievers. The proposed approach outperforms existing baselines with respect to both dense retriever selection and ranking. We make our code and results publicly available at https://github.com/ielab/larmor/.