Existing, fully supervised methods for person re-identification (ReID) require annotated data acquired in the target domain in which the method is expected to operate. This includes the IDs as well as images of persons in that domain. This is an obstacle in the deployment of ReID methods in novel settings. For solving this problem, semi-supervised or even unsupervised ReID methods have been proposed. Still, due to their assumptions and operational requirements, such methods are not easily deployable and/or prove less performant to novel domains/settings, especially those related to small person galleries. In this paper, we propose a novel approach for person ReID that alleviates these problems. This is achieved by proposing a completely unsupervised method for fine tuning the ReID performance of models learned in prior, auxiliary domains, to new, completely different ones. The proposed model adaptation is achieved based on only few and unlabeled target persons' data. Extensive experiments investigate several aspects of the proposed method in an ablative study. Moreover, we show that the proposed method is able to improve considerably the performance of state-of-the-art ReID methods in state-of-the-art datasets.