In a context of rapid global change, one of the key components for the survival of species is their genetic evolutionary potential for adaptation. Many methods have been developed to identify genetic variants underpinning adaptation to climate, but few tools were made available to integrate this knowledge into conservation management. We present here the SPatial Areas of Genotype probability (SPAG), a method to transpose the results of genotype-environment association studies into an evolutionary potential spatial prediction framework. We define a univariate model predicting the spatial distribution of a single-locus adaptive genotype and three multivariate models allowing the integration of several adaptive loci in a composite genotype. Unlike existing methods, SPAGs provide (a) a flexible approach to combine loci under different types of intergenic relationships and (b) a cross-validation framework to assess the pertinence of evolutionary potential predictions. SPAGs can be integrated with climate change projections to forecast the future spatial distribution of genotypes. The analysis of the mismatch between current and future SPAGs ("genomic offset") makes it possible to identify vulnerable populations potentially lacking the adaptive genotypes necessary for future survival. We tested the SPAG approach on a simulated population and applied it to characterize the evolutionary potential of 161 Moroccan goats to bioclimatic conditions. We identified seven regions of the Moroccan goat genome strongly associated with the precipitation seasonality and used the SPAG approach to predict the evolutionary potential. We then forecasted the shift in SPAGs under a strong climate change scenario and uncovered the goat populations likely to be threatened in future conditions. The SPAG methodology is an efficient and flexible tool to characterize the evolutionary potential across a landscape and to transpose evolutionary information into conservation frameworks.