Most of the modern technological applications we use in our daily life originate from the progress of Nanoscience–Nanotechnology (NST). The projection, showing the great impact that these advances are going to have on society, exhorts science education researchers to incorporate the modern field into educational contexts. Among the several issues that have to be dealt with, NST’s educational significance comes to the fore. This pilot study aims to examine whether both nano-trained primary school teachers and nano-trained students acknowledge the need for the inclusion of the NST content to school contexts. Fourteen primary school teachers and ten students, after their participation in an NST training course, were interviewed in order to provide their justifications. The results show that the vast majority of the participants acknowledge the educational significance of NST. The main arguments were associated with career possibilities, the relevance of the content to everyday life, and the need for nanoliteracy attainment. The results of this study can be used by NST education researchers in order to formulate a NST content structure for primary school nanoeducation.