The construction sector significantly impacts the environment. Buildings and non-building structures require natural resources and technical nutrients to be constructed and maintained. One of the most important challenges is the mitigation of their usage for construction projects. In the context of insufficient knowledge about the most effective leadership patterns for sustainable construction projects, one may wonder if there is one dominant style of management represented by construction companies. In turn, the challenges faced by these organizations can be related to how to effectively implement the circular economy (CE) concept, and thus reduce the negative externalities of the construction industry. Transition to sustainable construction requires the involvement of change leaders. In this article, based on a literature review and questionnaire, it was revealed that it is extremely difficult to distinguish one prevailing leadership style in construction companies. Besides, a path to CE maturity has been shown as a continual pursuit. The consistency enables effective promotion of the concept of CE in the construction company. The research allowed the identification of three explicit phases, disharmony, euphoria, and harmony, in becoming the CE-matured construction enterprise.