By using first-principles density functional theory calculations for (LaNiO3)(m)/(SrTiO3)(n) superlattices, we report a systematic electronic response to the interface geometry. It is found that the density of states at the Fermi level of metallic nickelate layers is significantly reduced without charge transfer in the vicinity of the interface to the insulating SrTiO3. This type of electronic state redistribution is clearly distinctive from other interface phenomena such as charge and orbital reconstruction. Our result sheds new light on the understanding of the nickelates and other transition-metal oxide heterostructures.