We report large-scale molecular dynamics simulations of the glass formation from the liquid phase and homogeneous nucleation phenomena of pure zirconium. For this purpose, we have built a modified embedded atom model potential in order to reproduce relevant structural, dynamic, and thermodynamic properties from ab initio and experimental data near the melting point. By means of liquid-solid interface simulations, we show that this potential provides a thermodynamic melting temperature and densities of the solid and liquid state in good agreement with experiments. Using melt-quenching simulations with one million atoms, we determine the glass transition from the temperature evolution of the inherent structure energy as well as the nose of the time-temperature-transformation curve located in the deep undercooling regime. We identify the local structural origin of the glass-forming ability as a competition between bcc and fivefold polytetrahedral structures that may represent an impediment of rapid homogeneous nucleation at such high undercoolings. This suggests the ability of single elemental zirconium to form a glass from the melt with cooling rates of at least ${10}^{12}\phantom{\rule{4pt}{0ex}}\mathrm{K}/\mathrm{s}$, compatible with modern experiments.