An approach to the selection of glasses for the formation of GRIN structures was proposed and verified using a set of designed glasses and numerical simulation of the structures. This set presented aluminum–boron silicate glasses with a high content of alkaline ions. Low-temperature (below glass transition) silver ion exchange in these glasses was characterized by integrated optics technique. A high index variation (up to 0.21), and fast diffusion (up to diffusion depth of 140 μm after 30-min processing at 400 °C) had been found to make these glasses attractive from the viewpoint of their application to the formation of GRIN structures. Concentration dependences of the diffusion coefficient (diffusion nonlinearity) of the glasses were determined and studied, for the character of these dependences strongly influences the quality of GRIN structures formed. Diffusion nonlinearity was analyzed by comparing both concentration dependences of the diffusion coefficients of different glasses and normalized index variation profiles with the closest erfc-function. The latter was done using specific plots δ n via erf( x / d ), where x is the coordinate measured from the glass surface to the bulk, d is the characteristic diffusion depth, and δ n is the difference between normalized index variation profile and the closest erfc-function. These plots allowed selecting among the designed glasses the ones, which were the most suitable for the formation of rod and slab GRIN lenses. The correctness of this selection and applicability of the selected glasses to the formation of slab and rod GRIN lenses was verified through simulating both ion-exchange process and optical performance of the GRIN lenses. The proposed approach presents a simple technique for working out recommendations on diffusion nonlinearity of glasses for different types of GRIN structures and for deducing the influence of glass composition on diffusion properties of glasses.