Interactions between the introduced gray squirrel (Sciurus carolinensis) and the native red squirrel (S. vulgaris) play an important role in the ecological equilibrium of European forest ecosystems. However, the range dynamics of the grey squirrel and red squirrel under future climate change scenarios remain unknown. The present study examined the range dynamics of grey squirrels and red squirrels in Europe and their range overlap now and in the future based on climate change. Under the most optimistic climate change scenario (SSP126), expansion of the grey squirrel’s range was mainly predicted in Germany, France, Croatia, Serbia, and Bulgaria. Under the most pessimistic climate change scenario (SSP585), expansion of the grey squirrel’s range was predicted in vast and scattered regions. Additionally, France, Italy, and Germany were overlapping ranges for the grey squirrel and red squirrel in the future under the SSP126 scenario but not under the current conditions, suggesting that there will be new regions where grey squirrels may threaten red squirrels in the future under SSP126. The range overlaps under the SSP585 scenario but not under the current conditions were vast and scattered, suggesting that there will be new regions in the future where grey squirrel may displace red squirrels under SSP585. Despite considerable variation, we detected expansions in the grey squirrel and red squirrel ranges and an increase in overlapping ranges between grey squirrels and red squirrels in the future. Therefore, our prediction suggests increasing threats of grey squirrels toward red squirrels in Europe in the future under climate change, which may impact the ecological equilibrium of European forest ecosystems.