Unsupervised learning on 3D point clouds has undergone a rapid evolution, especially thanks to data augmentation-based contrastive methods. However, data augmentation is not ideal as it requires a careful selection of the type of augmentations to perform, which in turn can affect the geometric and semantic information learned by the network during self-training. To overcome this issue, we propose an augmentation-free unsupervised approach for point clouds to learn transferable point-level features via soft clustering, named SoftClu. SoftClu assumes that the points belonging to a cluster should be close to each other in both geometric and feature spaces. This differs from typical contrastive learning, which builds similar representations for a whole point cloud and its augmented versions. We exploit the affiliation of points to their clusters as a proxy to enable self-training through a pseudo-label prediction task. Under the constraint that these pseudo-labels induce the equipartition of the point cloud, we cast SoftClu as an optimal transport problem, which can be solved by using an efficient variant of the Sinkhorn-Knopp algorithm. We formulate an unsupervised loss to minimize the standard cross-entropy between pseudo-labels and predicted labels. Experiments on downstream applications, such as 3D object classification, part segmentation, and semantic segmentation, show the effectiveness of our framework in outperforming state-of-the-art techniques.