The construction sector contributes substantially to the consumption of raw materials and the production of waste. Traditional building design strategies are based on an unsustainable economic linear model. Transition to the circular economy (CE) paradigm aims to reduce the consumption of raw materials and minimise waste. To achieve the promises of CE, it is crucial to assess sustainability aspects early. In the final design decision-making process, both technical circularity and sustainability strategies must be implemented. However, the existing building circularity assessment (BCA) models and tools are not comprehensive and fail to cover all the critical factors that affect circularity and sustainability in the built environment. Technical circularity and sustainability assessments are often conducted in isolation. There is a need for practical comprehensive assessment tools for use during the early design stage of construction projects, where crucial decisions are made as opposed to the late design stages, in which changes are more costly and complex. Since BCA requires a large amount of data, it requires the use of a supplementary tool to conduct the assessment effectively. Building information modelling (BIM) can serve as a useful tool to facilitate BCA. This paper proposes a framework that integrates technical circularity and sustainability aspects, such as environmental impact by life cycle assessment (LCA) and economic aspect by life cycle costing (LCC) within the BIM environment to achieve a sustainable circular-built environment. The framework is a promising step toward developing a prototype tool that assesses circularity and sustainability aspects simultaneously and helps decision-making for designers in the context of building design and material selection and trade-offs between the different aspects and selects more circular and sustainable alternatives. The proposed framework aims to contribute positively to reducing global warming and decarbonization in the building sector and the shift toward a sustainable circular-built environment.