A framework for identifying species that may become invasive under future climate conditions is presented, based on invader attributes and biogeography in combination with projections of future climate. We illustrate the framework using the CLIMEX niche model to identify future climate suitability for three species of Hawkweed that are currently present in the Australian Alps region and related species that are present in the neighbouring region. Potential source regions under future climate conditions are identified, and species from those emerging risk areas are identified. We use dynamically downscaled climate projections to complement global analyses and provide fine-scale projections of suitable climate for current and future (2070–2099) conditions at the regional scale. Changing climatic conditions may reduce the suitability for some invasive species and improve it for others. Invasive species with distributions strongly determined by climate, where the projected future climate is highly suitable, are those with the greatest potential to be future invasive species in the region. As the Alps region becomes warmer and drier, many more regions of the world become potential sources of invasive species, although only one additional species of Hawkweed is identified as an emerging risk. However, in the longer term, as the species in these areas respond to global climate change, the potential source areas contract again to match higher altitude regions. Knowledge of future climate suitability, based on species-specific climatic tolerances, is a useful step towards prioritising management responses such as targeted eradication and early intervention to prevent the spread of future invasive species.