Transient radio frequency interference (RFI) is detrimental to radio astronomy. It is particularly difficult to identify the sources of transient RFI, which is broadband and intermittent. Such RFI is often generated by devices like mechanical relays, fluorescent lighting or AC machines, which may be present in the surrounding infrastructure of a radio telescope array. One mitigating approach is to deploy independent RFI monitoring stations at radio telescope arrays. Once the sources of RFI signals are identified, they may be removed or replaced where possible. For the first time in the open literature, we demonstrate an approach to classifying the sources of transient RFI (in time domain data) that makes use of deep learning techniques including CNNs and LSTMs. Applied to a previously obtained dataset of experimentally recorded transient RFI signals, our proposed approach offers good results. It shows potential for development into a tool for identifying the sources of transient RFI signals recorded by independent RFI monitoring stations.