This is reported by Euronews.
According to an unnamed interlocutor, European Legal Commissioner Didier Reinders said that EU member states can vaccinate their residents with any vaccines, but then they will not be able to receive a vaccination passport as a potential pass for free travel. They associate this with the fact that the European Union is not sure about the quality of these vaccines.
At the same time, at this stage, the main challenges for the European Commission regarding future vaccination passports are data protection and discrimination issues. Since not all people can get vaccinated on time, they are vaccinated on a special schedule.
Note that there are currently four vaccines approved in the EU — Pfizer / BioNtech, AstraZeneca, Moderna, and Johnson & Johnson (Janssen).