The non-structural protein NS1 of influenza A viruses is considered to be the major antagonist of the interferon system and antiviral defenses of the cell. It could therefore represent a suitable target for novel antiviral strategies. As a first step towards the identification of small compounds targeting NS1, we here investigated the druggable potential of its RNA-binding domain since this domain is essential to the biological activities of NS1. We explored the flexibility of the full-length protein by running molecular dynamics simulations on one of its published crystal structures. While the RNA-binding domain structure was remarkably stable along the simulations, we identified a flexible site at the two extremities of the "groove" that is delimited by the antiparallel α-helices that make up its RNA-binding interface. This groove region is able to form potential binding pockets, which, in 60% of the conformations, meet the druggability criteria. We characterized these pockets and identified the residues that contribute to their druggability. All the residues involved in the druggable pockets are essential at the same time to the stability of the RNA-binding domain and to the biological activities of NS1. They are also strictly conserved across the large sequence diversity of NS1, emphasizing the robustness of this search towards the identification of broadly active NS1-targeting compounds.