Over the last few decades, there is a remarkable increase in air traffic worldwide; however, despite of rapid technological development and improved airport infrastructure, there is still an increasing number of aviation accidents and fatalities. In order to meet safety demands of Air Traffic Control (ATC), Machine Learning (ML) based aircraft conflict detection techniques are focused to predict events before they come to reality. This research presents a systematic literature review (SLR) about the applications of ML techniques in safety prediction of ATC system. Initially, the existing aircraft conflict prediction models are classified into three broad categories; logical, geometric and probabilistic. A formal process of SLR is then conducted which is initiated with preprocessing and effective searching. A series of filtering called title, abstract and objective-based are then applied to extract the most relevant articles. Detailed and critical reviews of selected articles are performed to identify challenges which are segregated into dataset, model and evaluation techniques, furthermore, the optimal solutions for each are proposed. Finally the matrices to map the identified challenged with their proposed solutions are constructed. This research serves as a foundation for future research and towards integration of ML based safety prediction techniques into modern ATC system.