We consider the problem of user equipment (UE) positioning based on radio signals via deep learning. As in most supervised-learning tasks, a critical aspect is the availability of a relevant dataset to train a model. However, in a cellular network, the data-collection step may induce a high communication overhead. As a result, to reduce the required size of the dataset, it may be interesting to carefully choose the positions to be labelled and to be used in the training. We therefore propose an active learning approach for efficient data collection. We first show that significant gains (both in terms of positioning accuracy and size of the required dataset) can be obtained for the considered positioning problem using a genie. This validates the interest of active learning for positioning. We then propose a \textcolor{blue}{practical} method to approximate this genie.