In the last two decades, there have been many calls to integrate sustainability into projects. However, there are conflicting views about the relationship between sustainability and project success. Some contend that project sustainability could adversely affect project success, while others maintain the contrary. Yet, the exploration of this relationship has been insufficient thus far. Notably, no existing work specifically investigates this relationship within the software domain. Therefore, this paper aims to contribute significantly by introducing a conceptual framework that assists in inspecting the relationships between software project sustainability (SPS) and project success. The proposed framework was developed based on well-defined aspects of both concepts. The findings show that most of the relationships between the two concepts are expected to be significant and positive. Our propositions were built after analysing the best of relevant contributions. However, an empirical examination is needed, especially with the presence of control variables such as country, company size, and project complexity. This work could be an initial motion for future empirical studies and provide a significant theoretical foundation for researchers and practitioners in this domain.