Multichannel processing is widely used for speech enhancement but several limitations appear when trying to deploy these solutions to the real-world. Distributed sensor arrays that consider several devices with a few microphones is a viable alternative that allows for exploiting the multiple devices equipped with microphones that we are using in our everyday life. In this context, we propose to extend the distributed adaptive node-specific signal estimation approach to a neural networks framework. At each node, a local filtering is performed to send one signal to the other nodes where a mask is estimated by a neural network in order to compute a global multi-channel Wiener filter. In an array of two nodes, we show that this additional signal can be efficiently taken into account to predict the masks and leads to better speech enhancement performances than when the mask estimation relies only on the local signals.