In reverberant conditions with a single speaker, each far-field microphone records a reverberant version of the same speaker signal at a different location. In over-determined conditions, where there are multiple microphones but only one speaker, each recorded mixture signal can be leveraged as a constraint to narrow down the solutions to target anechoic speech and thereby reduce reverberation. Equipped with this insight, we propose USDnet, a novel deep neural network (DNN) approach for unsupervised speech dereverberation (USD). At each training step, we first feed an input mixture to USDnet to produce an estimate for target speech, and then linearly filter the DNN estimate to approximate the multi-microphone mixture so that the constraint can be satisfied at each microphone, thereby regularizing the DNN estimate to approximate target anechoic speech. The linear filter can be estimated based on the mixture and DNN estimate via neural forward filtering algorithms such as forward convolutive prediction. We show that this novel methodology can promote unsupervised dereverberation of single-source reverberant speech.