In recent decades, universities have undergone remarkable development in terms of awareness of the relevance of entrepreneurship. Potential entrepreneurship or entrepreneurial intention (EI) is the first step in the entrepreneurial process, but further research is needed on the antecedents of EI. There is a gap in the literature concerning the antecedents of EI and how they are formed. The present study responds to this need for future research. Under the paradigm of Entrepreneurial University, the present research analyzes the antecedents of students’ entrepreneurial potential from a competency-based approach. With a SEM model the effect of six different competences on EI are measured, considering also the three mediating dimension of the Theory of Planned Behaviour (TPB). The results of the present study offer support for using TPB to understand intention formation, as the three dimensions explain EI with the highest level of significance. The results suggest that the entrepreneurial competences should each be specifically treated, as their effects on EI differ both in relation to their total effects and in terms of individual indirect effects. It is worth mentioning that differences between mediators are also noted. In line with the increasing awareness of universities regarding their role as promoters of entrepreneurship and their consequent responsibility in generating entrepreneurial human capital, the results of this study have relevant practical implications. On the one hand, focusing on the educational impact, the results highlighted the relevance of competence training to increase the entrepreneurial potential of students. Moreover, the results provide information on the competences to be developed to promote each TPB dimension. Thus, the results can guide and inspire educators involved in both the design and delivery of entrepreneurship training at the university level or in other educational contexts.