The brain comprises a complex system of neurons interconnected by an intricate network of anatomical links. While recent studies demonstrated the correlation between anatomical connectivity patterns and gene expression of neurons, using transcriptomic information to automatically predict such patterns is still an open challenge. In this work, we present a completely data-driven approach relying on machine learning (i.e., neural networks) to learn the anatomical connection directly from a training set of gene expression data. To do so, we combined gene expression and connectivity data from the Allen Mouse Brain Atlas to generate thousands of gene expression profile pairs from different brain regions. To each pair, we assigned a label describing the physical connection between the corresponding brain regions. Then, we exploited these data to train neural networks, designed to predict brain area connectivity. We assessed our solution on two prediction problems (with three and two connectivity class categories) involving cortical and cerebellum regions. As demonstrated by our results, we distinguish between connected and unconnected regions with 85% prediction accuracy and good balance of precision and recall. In our future work we may extend the analysis to more complex brain structures and consider RNA-Seq data as additional input to our model.