It is often assumed that the data is readily available for processing at a single, secure, and trusted location. However, in reality, data needs to be collected and (pre)processed; furthermore, a single, secure, trusted location might not exist, for example, if multiple organizations can not agree on a location or moving data out of organizational boundaries is prohibited. In this paper, we discuss the privacy implications of collecting and (pre)processing data in the field of process mining. We introduce two use cases for distributed process mining and define an adversary model. Based on this, we discuss possible guarantees that might be given independent of the data and metrics to empirically measure the achieved privacy in a real-world setting.