For ²⁷Al nuclei in Al₂O₃ crystals, both nominally pure and doped with Cr³⁺, suppression of the impurity nuclear spin-lattice relaxation under the condition of additional stationary magnetic saturation of the NMR line has been observed for the first time. Measurements of the lattice and impurity components of the spin-lattice relaxation time have been performed. The study was carried out at 77 K for different crystal orientations. Possible mechanisms of the impurity NMR relaxation suppression are discussed.