In recent years, a significant number of self-adaptive systems (i.e.: systems capable of knowing what is happening about themselves, and consequently partially implementing the quality of awareness) have been developed. The literature has extensively researched the use of goal oriented requirements engineering and the use of the MAPE (Monitor-Analyze-Plan-Execute) reference architecture for the development of self-adaptive systems. However, building such systems based on reference strategies is not trivial, it can result in structural problems that negatively impact some quality attributes of the final product (e.g.: reusability, modularity, modifiability and understandability). In this context, reengineering strategies for the reorganization of such systems are poor explored, and they are limited to recovering and restructuring the logic of adaptation in low-level models. This approach keeps the difficulty of treating the awareness quality as a first-class non-functional re-quirement (NFR) directly affecting architecture selection and implementation of the system. Our research aims to mitigate this problem through a strategy of reengi-neering self-adaptive systems, centered on software awareness as an NFR. This strategy will assist in the removal of some recurring problems in the implementation of MAPE according to the literature. The reengineering strategy is organized into four sub-processes: (A) recover the intentionality of the system with an emphasis on its awareness goals, generating an AS-IS goal model; (B) specify the TO-BE goal model by reusing a set of SRconstructs to operationalize the software awareness NFR according to the MAPE standard; (C) redesign the system by reviewing the operationalizations of awareness and selecting the technologies to implement the MAPE, and; (D) finally, reimplement the system according to a new structure, add-ing code metadata to maintain traceability for the self-adaptation mechanism in or-der to facilitate new evolutions. The scope of our research is object-oriented (OO) self-adaptive systems using the i framework as a language for goal-oriented models. Our results of evaluations, for OO self-adaptive systems developed in Java for mobile devices with Android, show that the strategy helps in realigning the system with the best practices recommended by the, facilitating future developments.