Digital product passports (DPP) have been proposed in the European Ecodesign for Sustainable Products Regulation (ESPR) as a means to keep and provide product information that facilitates product reusage, reparation, and recycling. Thus, DPPs should provide a positive effect on the environmental impact of future manufactured products, preventing waste and promoting a circular economy (CE) model. ESPR settles a set of requirements in collecting and administering product-related data. Decentralised identifiers (DID) and verifiable credentials (VC) are two self-sovereign-identity-related elements that may help in that DPP management since they introduce a decentralised administration of identity that may enhance the overall scalability of the resulting system, improving also its reliability. This paper analyses the ESPR requirements and describes how they may be achieved using DIDs and VCs, assessing their performance in some scenarios.