Business process compliance is a key area of business process management and aims at ensuring that processes obey to compliance constraints such as regulatory constraints or business rules imposed on them. Process compliance can be checked during process design time based on verification of process models and at runtime based on monitoring the compliance states of running process instances. For existing compliance monitoring approaches it remains unclear whether and how compliance violations can be predicted, although predictions are crucial in order to prepare and take countermeasures in time. This work, hence, analyzes existing literature from compliance monitoring as well as predictive process monitoring and provides an updated framework of compliance monitoring functionalities. Moreover, it raises the vision of a comprehensive predictive compliance monitoring system that integrates existing predicate prediction approaches with the idea of employing PPM with different prediction goals such as next activity or remaining time for prediction and subsequent mapping of the prediction results onto the given set of compliance constraints (PCM). For each compliance monitoring functionality we elicit PCM system requirements and assess their coverage by existing approaches. Based on the assessment, open challenges and research directions realizing a comprehensive PCM system are elaborated.