Image clustering is a particularly challenging computer vision task, which aims to generate annotations without human supervision. Recent advances focus on the use of self-supervised learning strategies in image clustering, by first learning valuable semantics and then clustering the image representations. These multiple-phase algorithms, however, increase the computational time and their final performance is reliant on the first stage. By extending the self-supervised approach, we propose a novel single-phase clustering method that simultaneously learns meaningful representations and assigns the corresponding annotations. This is achieved by integrating a discrete representation into the self-supervised paradigm through a classifier net. Specifically, the proposed clustering objective employs mutual information, and maximizes the dependency between the integrated discrete representation and a discrete probability distribution. The discrete probability distribution is derived though the self-supervised process by comparing the learnt latent representation with a set of trainable prototypes. To enhance the learning performance of the classifier, we jointly apply the mutual information across multi-crop views. Our empirical results show that the proposed framework outperforms state-of-the-art techniques with the average accuracy of 89.1% and 49.0%, respectively, on CIFAR-10 and CIFAR-100/20 datasets. Finally, the proposed method also demonstrates attractive robustness to parameter settings, making it ready to be applicable to other datasets.