Multiple synthetic data generation models have emerged, among which deep learning models have become the vanguard due to their ability to capture the underlying characteristics of the original data. However, the resemblance of the synthetic to the original data raises important questions on the protection of individuals' privacy. As synthetic data is perceived as a means to fully protect personal information, most current related work disregards the impact of re-identification risk. In particular, limited attention has been given to exploring outliers, despite their privacy relevance. In this work, we analyze the privacy of synthetic data w.r.t the outliers. Our main findings suggest that outliers re-identification via linkage attack is feasible and easily achieved. Furthermore, additional safeguards such as differential privacy can prevent re-identification, albeit at the expense of the data utility.