Human leishmaniasis is a neglected tropical disease which affects nearly 1.5 million people every year, with Mexico being an important endemic region. One of the major defense mechanisms of these parasites is based in the polyamine metabolic pathway, as it provides the necessary compounds for its survival. Among the enzymes in this route, trypanothione reductase (TryR), an oxidoreductase enzyme, is crucial for the Leishmania genus’ survival against oxidative stress. Thus, it poses as an attractive drug target, yet due to the size and features of its catalytic pocket, modeling techniques such as molecular docking focusing on that region is not convenient. Herein, we present a computational study using several structure-based approaches to assess the druggability of TryR from L. mexicana, the predominant Leishmania species in Mexico, beyond its catalytic site. Using this consensus methodology, three relevant pockets were found, of which the one we call σ-site promises to be the most favorable one. These findings may help the design of new drugs of trypanothione-related diseases.