The focus of project management on processes and activities in the construction sector presents high variability and uncertainty. This article suggests the adoption of agile methodologies with an emphasis on people as an alternative that encourages reflection and anticipation of building maintenance and demolition problems. The objective is to identify the theoretical proximity between the main characteristics of agile construction project management and the circular economy mindset. The methodology used was a systematic bibliographical review and state-of-the-art content analysis on the application of agile in construction projects, with the discovery of the most cited characteristics and, subsequently, the establishment of a correlation with the elements of the circular economy mindset from inferences regarding the similarity of concepts and perspectives between both. From this analysis emerges the synergy between the circular and agile mindset. The conclusive trend is that architecture and construction benefit from the transitions from traditional management methodology to agile management and from the linear economy to the circular economy, given its limited technological stage in Brazil, in addition to the possibility of reducing waste generation and maintenance of the added value of buildings.