Cognitive Digital twins (CDT) are Digital Twins with cognition capabilities and ensure a proper monitoring and optimization of a specific asset's behaviour. In the context of supply chains, there are different entities involved from assets, processes, up to organizations, which can be modelled as CDTs that collaborate each other, share and process information, learn and optimize behaviour to improve supply chain sustainability. This paper emphasises on the concept of supply chain CDT and proposes a holistic governance approach integrating three different views: i) business and sustainability; ii) data governance and ii) cognition (AI) models gover-nance. A detailed description of the main questions/ issues for each of the three views is provided along with an example of how it can be modelled in a case of a product with different circular strategies of its critical components.