Face recognition has been one of the most relevant and explored fields of Biometrics. In real-world applications, face recognition methods usually must deal with scenarios where not all probe individuals were seen during the training phase (openset scenarios). Therefore, open-set face recognition is a subject of increasing interest as it deals with identifying individuals in a space where not all faces are known in advance. This is useful in several applications, such as access authentication, on which only a few individuals that have been previously enrolled in a gallery are allowed. The present work introduces a novel approach towards open-set face recognition focusing on small galleries and in enrollment detection, not identity retrieval. A Siamese Network architecture is proposed to learn a model to detect if a face probe is enrolled in the gallery based on a verification-like approach. Promising results were achieved for small galleries on experiments carried out on Pubfig83, FRGCv1 and LFW datasets. State-ofthe-art methods like HFCN and HPLS were outperformed on FRGCv1. Besides, a new evaluation protocol is introduced for experiments in small galleries on LFW.