In the context of stagnation or negative natural population growth, internal and international migration increasingly influence population structure and composition alongside natural processes such as aging and falling birth rates. However, a territory’s ability to attract new residents, particularly foreigners, depends on various factors, including population mobility, natural growth dynamics, and local economic conditions. The demographic and economic evolution of 7,609 Italian municipalities is analyzed between 2001 and 2021 with the aim of explaining the spatial distribution of the foreign population. Forecasts for the proportion of the foreign population resident in each municipality are obtained for two years out of the sample, based on explanatory variables that reflect territorial attractiveness, namely net internal and international migration, the natural population growth rate, and average municipal income. These indicators, reflecting local demographic and economic vitality, help to explain why some municipalities attract a larger foreign population than others. Using a blind separation model of space-time sources (ST-BSS), the latent factors driving demographic evolution in space and time are identified. The analysis aims to provide interpretative and prospective tools to inform more targeted local policies capable of capturing the multi-scalar and territorially differentiated nature of migratory phenomena.