Research in various fields is currently experiencing challenges regarding the reproducibility of results. This problem is also prevalent in machine learning (ML) research. The issue arises primarily due to unpublished data and/or source code and the sensitivity of ML training conditions. Although different solutions have been proposed to address this issue, such as using ML platforms, the level of reproducibility in ML-driven research remains unsatisfactory. Therefore, in this article, we discuss the reproducibility of ML-driven research with three main aims: (i) identify the barriers to reproducibility when applying ML in research as well as categorize the barriers to different types of reproducibility (description, code, data, and experiment reproducibility), (ii) identify potential drivers such as tools, practices, and interventions that support ML reproducibility as well as distinguish between technology-driven drivers, procedural drivers, and drivers related to awareness and education, and (iii) map the drivers to the barriers. With this work, we hope to provide insights and contribute to the decision-making process regarding the adoption of different solutions to support ML reproducibility.