The COVID-19 pandemic brought visibility and intensified the discussions on the European Union’s (EU) health mandate. The proposals of the European Commission (EC) to move towards a European Health Union (EHU) can be seen as a starting point towards more integration in health. However, the definition of what the EHU will look like is not clear. This paper searches to find a common definition, and/or features for this EHU through a systematic literature review performed in May 2021. “European Union’s concern about health for all” is suggested as a definition. The main drivers identified to develop an EHU are: surveillance and monitoring, crisis preparedness, funding, political will, vision of public health expenditures, population’s awareness and interest, and global health. Based on these findings, five scenarios were developed: making a full move towards supranational action; improving efficiency in the actual framework; more coordination but no real change; in a full intergovernmentalism direction; and fragmentation of the EU. The scenarios show that the development of a EHU is possible inside the current legal framework. However, it will rely on increased coordination and has a focus on cross-border health threats. Any development will be strongly linked to political choices from Member States.