Large-scale visual out-of-distribution (OOD) detection has witnessed remarkable progress by leveraging vision-language models such as CLIP. However, a significant limitation of current methods is their reliance on a pre-defined set of in-distribution (ID) ground-truth label names (positives). These fixed label names can be unavailable, unreliable at scale, or become less relevant due to in-distribution shifts after deployment. Towards truly unsupervised OOD detection, we utilize widely available text corpora for positive label mining, bypassing the need for positives. In this paper, we utilize widely available text corpora for positive label mining under a general concept mining paradigm. Within this framework, we propose ClusterMine, a novel positive label mining method. ClusterMine is the first method to achieve state-of-the-art OOD detection performance without access to positive labels. It extracts positive concepts from a large text corpus by combining visual-only sample consistency (via clustering) and zero-shot image-text consistency. Our experimental study reveals that ClusterMine is scalable across a plethora of CLIP models and achieves state-of-the-art robustness to covariate in-distribution shifts. The code is available at https://github.com/HHU-MMBS/clustermine_wacv_official.