We present a detailed analysis of the pre-edge peak present in the Al K-edge XANES spectra of corundum (α-Al₂O₃) and diaspore (α-AlOOH), as measured at room temperature. This is achieved by XANES and DOS calculations performed using the density functional theory in a pseudopotential plane-wave framework. The XANES calculations carried out for the equilibrium atomic positions do not reproduce the pre-edge of corundum and partially reproduce it in the case of diaspore. It is shown that the electronic transitions occuring in the pre-edge involves the 3s empty states of the aluminium absorbing atom. The Al 3s states can be probed in the electric dipole approximation via a p-s mixing, which is possible only if the Al site is not centrosymmetric. Although Al does not occupy an inversion center in the two minerals under study, the p-s mixing is too weak to provide a pre-edge feature in good agreement with experiment. The deviation from centrosymmetry can be enhanced by the atomic vibrations. We develop a theory that takes into account the atomic vibrations directly in the calculation of the absorption cross section, based on the Born-Oppenheimer approximation. This theory is applied to corundum and diaspore and yields satisfactory results in the pre-edge region.