In the field of functional genomics, the analysis of gene expression profiles through Machine and Deep Learning is increasingly providing meaningful insight into a number of diseases. The paper proposes a novel algorithm to perform Feature Selection on genomic-scale data, which exploits the reconstruction capabilities of autoencoders and an ad-hoc defined Explainable Artificial Intelligence-based score in order to select the most informative genes for diagnosis, prognosis, and precision medicine. Results of the application on a Chronic Lymphocytic Leukemia dataset evidence the effectiveness of the algorithm, by identifying and suggesting a set of meaningful genes for further medical investigation.