Background: One of the current challenges in higher education is the development of students’ emotional competencies, and consequently, how these competencies can be trained. Moreover, this must be addressed within the UN framework of inclusive, equitable, quality education (United Nations Agenda 2030; SDG 4). Methods: The present study the following objectives: (1) to study the degree of interest and the level of general knowledge that students studying for Education degrees perceive themselves to have; (2) to examine the perception of the participants of variables of emotional knowledge, according to their degree program and year of study; (3) to analyze the relationship between these emotional knowledge variables and perceived emotional intelligence (EI), using Spearman’s Rho test; and (4) to study the predictive capacity of the study variables on future teachers’ emotional knowledge variables through a linear regression analysis. The study sample contained a total of 434 university students from three degree programs at two universities in Spain. Two instruments were used: an ad hoc questionnaire, which assessed perceived emotional knowledge according to three variables (general knowledge of EI, where the level of training in EI is considered; intrapersonal knowledge of EI; and theoretical/practical knowledge related to teaching), and the Trait Meta-Mood Scale (TMMS-24), which assesses metaknowledge of emotional states (attention, clarity, and repair). Results: The results of this study show that there are differences in students’ self-perceived knowledge of EI depending on their course and degree, and indicate that students present high interest, while their perceived level of knowledge is low. In addition, emotional clarity is the EI variable that was identified as being important in the emotional knowledge of future teachers, and therefore, a key skill to stimulate in a theoretical/practical way during their initial training. Conclusion: This study shows evidence of the importance of social–emotional competencies in initial teacher training.