Context: Anticipating where an invasive species could become abundant can help guide prevention and control efforts aimed at reducing invasion impacts. Information on potential abundance can be combined with information on the current status of an invasion to guide management towards currently uninvaded locations where the threat of invasion is high. Objectives: We aimed to support management by developing predictive maps of potential cover for cheatgrass (Bromus tectorum), a problematic invader that can transform plant communities. We integrated our predictions of potential abundance with mapped estimates of current cover to quantify invasion potential within lightly invaded areas. Methods: We used quantile regression to model cheatgrass abundance as a function of climate, weather, and disturbance, treating outputs as low to high invasion scenarios. We developed a species-specific set of covariates and validated model performance using spatially and temporally independent data. Results: Potential cheatgrass abundance was higher in areas that had burned, at low elevations, and when fall germination conditions were more favorable. Our results highlight the extensive areas across the Great Basin where cheatgrass abundance could increase to levels that can alter fire behavior and cause other ecological impacts. Conclusions: We predict potential cheatgrass abundance to quantify relative invasion risk. Our model results provide high and low scenarios of cheatgrass abundance to guide resource allocation and planning efforts across shrubland ecosystems of the Great Basin that remain relatively uninvaded. Combining information on an invasive species’ current and potential abundance can yield spatial predictions to guide resource allocation and management action.