The transition toward a sustainable built environment requires construction material supply chains to integrate both carbon performance and circularity principles. However, existing frameworks tend to address these areas separately, carbon management focuses primarily on emissions reduction, while circular economy models emphasise material recovery and resource efficiency. This conceptual study aims to explore the convergence of these two perspectives to advance performance evaluation within construction material supply chains. A comprehensive review of academic and industry literature was undertaken, examining established tools and frameworks such as Life Cycle Assessment (LCA), Building Information Modelling (BIM), Environmental Product Declarations (EPDs), and sustainable procurement guidelines. The analysis identifies overlapping and complementary criteria and demonstrates how carbon and circularity indicators can be harmonised within supply chain evaluation models. Key dimensions emerging from the synthesis include embodied carbon, material circularity potential, design for disassembly, supplier transparency, and data integration across life cycle stages. Building on these insights, this study proposes a conceptual framework that links carbon accounting metrics with circularity indicators to enable holistic performance benchmarking. The integrated approach enhances supply chain traceability, supports informed procurement and design decisions, and aligns industry practices with evolving net zero and circular economy policies. By bridging these parallel sustainability agendas, the research establishes a theoretical foundation for developing next generation evaluation tools that balance emission reduction with material circularity. The framework offers valuable implications for industry practitioners, academics, and policymakers seeking to implement net zero and circular strategies within construction material supply chains, to build sustainable built environments.