Images of morphed faces pose a serious threat to face recognition--based security systems, as they can be used to illegally verify the identity of multiple people with a single morphed image. Modern detection algorithms learn to identify such morphing attacks using authentic images of real individuals. This approach raises various privacy concerns and limits the amount of publicly available training data. In this paper, we explore the efficacy of detection algorithms that are trained only on faces of non--existing people and their respective morphs. To this end, two dedicated algorithms are trained with synthetic data and then evaluated on three real-world datasets, i.e.: FRLL-Morphs, FERET-Morphs and FRGC-Morphs. Our results show that synthetic facial images can be successfully employed for the training process of the detection algorithms and generalize well to real-world scenarios.