Species introduction represents one of the most serious threats for biodiversity. The realized climatic niche of an invasive species can be used to predict its potential distribution in new areas, providing a basis for screening procedures in the compilation of black and white lists to prevent new introductions. We tested this assertion by modeling the realized climatic niche of the Eastern grey squirrel Sciurus carolinensis. Maxent was used to develop three models: one considering only records from the native range (NRM), a second including records from native and invasive range (NIRM), a third calibrated with invasive occurrences and projected in the native range (RCM). Niche conservatism was tested considering both a niche equivalency and a niche similarity test. NRM failed to predict suitable parts of the currently invaded range in Europe, while RCM underestimated the suitability in the native range. NIRM accurately predicted both the native and invasive range. The niche equivalency hypothesis was rejected due to a significant difference between the grey squirrel's niche in native and invasive ranges. The niche similarity test yielded no significant results. Our analyses support the hypothesis of a shift in the species' climatic niche in the area of introductions. Species Distribution Models (SDMs) appear to be a useful tool in the compilation of black lists, allowing identifying areas vulnerable to invasions. We advise caution in the use of SDMs based only on the native range of a species for the compilation of white lists for other geographic areas, due to the significant risk of underestimating its potential invasive range.