All sectors have been affected by digital, economic, and demographic transitions. These will also be completely changing the paradigms of the construction industry, which is increasingly being pressured to implement strategic solutions in order to mitigate its own current environmental impact. Existing environmental standards and voluntary protocols are useful tools for reducing the environmental impact of buildings and infrastructures above all during the operation phase, but there is no consistent methodology for creating a circular and sustainable construction stage at the moment, probably because this represents a small stage in the entire life cycle of a structure; nevertheless, the construction industry impacts a lot on the environment and should be managed in a circular way. A detailed analysis of the current problem is provided, as well as a potential solution involving a transition to a circular economic model for the entire construction lifecycle, supported by innovative models and methodologies. The purpose of this article is to create a “Circular Construction Sites” (CCS) flow using circular concepts and to develop a circular methodology for construction sustainability, considering practical solutions related to materials, water, and waste management. According to the circular economy model, the circular construction site can communicate with other industrial ecosystems to promote external circularity and zero waste production. A set of potential key performance indicators (KPIs) for monitoring circularity processes is presented. Finally, a method is proposed that circularizes not only the building or infrastructure design, but also the construction phase.