Universities are increasingly being asked to contribute to addressing the significant local and global challenges, such as those identified in the 2030 Agenda. Set in this framework, universities need to account for the social value they generate through their activities, particularly from the perspective of their contribution to different stakeholders. This approach requires, first of all, that the main stakeholders are identified. Relationship and dialogue mechanisms then need to be established which can help guide universities to choose activities which can better meet the needs of their stakeholders. The current paper analyses the potential of integrated reports, and triple bottom line reports, as an instrument for reporting on aspects that go beyond the financial sphere, including economic, social and environmental aspects. Specifically, the paper focuses on studying the viability of the Global Reporting Initiative (GRI) for reporting the value that European universities generate for their stakeholders. The results show, firstly, that the universities in the sample do not sufficiently address these questions in their reports. Internal stakeholders are prominent in their reports, with the interaction between them and the universities being generally unidirectional. References to value generated are limited, and usually refer to the economic value. However, some examples of good practices are identified that could be used to improve standards of reporting, especially in universities committed to integrated reporting initiatives, in order to better reflect the social value.