To contribute to small and medium enterprises’ (SMEs) sustainable transition into the circular economy, the study proposes the activation of organizational learning (OL) processes—denoted here as multi-level knowledge creation, transfer, and retention processes—as a key phase in introducing circular business models (CBMs) at SME and supply chain (SC) level. The research employs a mixed-method approach, using the focus group methodology to identify contextual elements impacting on CBM-related OL processes, and a survey-based evaluation to single out the most frequently used OL processes inside Italian construction SMEs. As a main result, a CBM-oriented OL multi-level model offers a fine-grained understanding of contextual elements acting mutually as barriers and drivers for OL processes, as possible OL dynamics among them. The multi-level culture construct—composed of external stakeholders’, SC stakeholders’, and organizational culture—identify the key element to activate CBM-oriented OL processes. Main implications are related to the identification of cultural, structural, regulatory, and process contextual elements across the external, SC, and organizational levels, and their interrelation with applicable intraorganizational and interorganizational learning processes. The proposed model would contribute to an improved implementation of transitioning into the circular economy utilizing sustainable business models in the construction SMEs.