In Europe, especially in Mediterranean areas, the sheep has been traditionally exploited as a dual purpose species, with income from both meat and milk. Modernization of husbandry methods and the establishment of breeding schemes focused on milk production have led to the development of "dairy breeds." This study investigated selective sweeps specifically related to dairy production in sheep by searching for regions commonly identified in different European dairy breeds. With this aim, genotypes from 44,545 SNP markers covering the sheep autosomes were analysed in both European dairy and non-dairy sheep breeds using two approaches: (i) identification of genomic regions showing extreme genetic differentiation between each dairy breed and a closely related non-dairy breed, and (ii) identification of regions with reduced variation (heterozygosity) in the dairy breeds using two methods. Regions detected in at least two breeds (breed pairs) by the two approaches (genetic differentiation and at least one of the heterozygosity-based analyses) were labeled as core candidate convergence regions and further investigated for candidate genes. Following this approach six regions were detected. For some of them, strong candidate genes have been proposed (e.g. ABCG2, SPP1), whereas some other genes designated as candidates based on their association with sheep and cattle dairy traits (e.g. LALBA, DGAT1A) were not associated with a detectable sweep signal. Few of the identified regions were coincident with QTL previously reported in sheep, although many of them corresponded to orthologous regions in cattle where QTL for dairy traits have been identified. Due to the limited number of QTL studies reported in sheep compared with cattle, the results illustrate the potential value of selection mapping to identify genomic regions associated with dairy traits in sheep.