In this paper we introduce the idea of estimating local topology in wireless networks by means of crowdsourced user reports. In this approach each user periodically reports to the serving basestation information about the set of neighbouring basestations observed by the user. We show that, by mapping the local topological structure of the network onto states of increasing knowledge, a crisp mathematical framework can be obtained, which allows in turn for the use of a variety of user mobility models. Using a simplified mobility model we show how obtain useful upper bounds on the expected time for a basestation to gain full knowledge of its local neighbourhood, answering the fundamental question about which classes of network deployments can effectively benefit from a crowdsourcing approach.