It is today widely accepted that a healthy diet is very useful to prevent the risk for cancer or its deleterious effects. Nutrigenomics studies are therefore taking place with the aim to test the effects of nutrients at molecular level and contribute to the search for anti-cancer treatments. These efforts are expanding the precious source of information necessary for the selection of natural compounds useful for the design of novel drugs or functional foods. Here we present a computational study to select new candidate compounds that could play a role in cancer prevention and care. Starting from a dataset of genes that are co-expressed in programmed cell death experiments, we investigated on nutrigenomics treatments inducing apoptosis, and searched for compounds that determine the same expression pattern. Subsequently, we selected cancer types where the genes showed an opposite expression pattern and we confirmed that the apoptotic/nutrigenomics expression trend had a significant positive survival in cancer-affected patients. Furthermore, we considered the functional interactors of the genes as defined by public protein-protein interaction data, and inferred on their involvement in cancers and/or in programmed cell death. We identified 7 genes and, from available nutrigenomics experiments, 6 compounds effective on their expression. These 6 compounds were exploited to identify, by ligand-based virtual screening, additional molecules with similar structure. We checked for ADME criteria and selected 23 natural compounds representing suitable candidates for further testing their efficacy in apoptosis induction. Due to their presence in natural resources, novel drugs and/or the design of functional foods are conceivable from the presented results.