Density Functional Theory and Embedded Atom Method potential calculations of small self-interstitials clusters in the hexagonal close packed (hcp) structure of zirconium have been performed. It is shown that by adding two self-interstitials in the lattice, the most stable configuration is triangular and contained into the basal plane. This particular configuration has been found in density functional theory and embedded atom method potential simulations. The same work is done by inserting three self-interstitials and the triangular configuration is again found as the most stable one. The study continues by adding self-interstitials to the planar structure and by reaching seven in density functional theory and thirty in embedded atom method potential calculations. The planar defect keeps a triangular configuration until seven self-interstitials, and beyond this amount, the triangle collapses by its summits into a hexagonal configuration. By considering it, an energetic model is proposed to describe the planar defect from two to seven self-interstitials. The stability of the identified configurations and the energetic model proposed constitute an important element to take into account when predicting the microstructural evolution of zirconium-based materials under irradiation.