Language-Assisted Image Clustering (LAIC) augments the input images with additional texts with the help of vision-language models (VLMs) to promote clustering performance. Despite recent progress, existing LAIC methods often overlook two issues: (i) textual features constructed for each image are highly similar, leading to weak inter-class discriminability; (ii) the clustering step is restricted to pre-built image-text alignments, limiting the potential for better utilization of the text modality. To address these issues, we propose a new LAIC framework with two complementary components. First, we exploit cross-modal relations to produce more discriminative self-supervision signals for clustering, as it compatible with most VLMs training mechanisms. Second, we learn category-wise continuous semantic centers via prompt learning to produce the final clustering assignments. Extensive experiments on eight benchmark datasets demonstrate that our method achieves an average improvement of 2.6% over state-of-the-art methods, and the learned semantic centers exhibit strong interpretability. Code is available in the supplementary material.