In this paper we propose a deep neural-network-based feature extraction scheme with the purpose of reducing the privacy risks encountered in speaker classification tasks. For this we choose a challenging scenario where we wish to perform gender recognition but at the same time prevent an attacker who has intercepted the features to perform speaker identification. Our approach is to employ Siamese training in order to obtain a feature representation that minimizes the Euclidean distance between same gender speakers while maximizing it for different gender speakers. It is experimentally shown that the obtained effect is of anonymizing speakers from the same gender class and thus drastically reducing privacy risks while still permitting class discrimination with a higher accuracy than other previously investigated methods.