The 2019 novel coronavirus disease (COVID-19) that emerged in China has been declared as public health emergency of international concern by the World Health Organization and the causative pathogen was named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In this report, we analyzed the structural characteristics of the N-terminal domain of the S1 subunit (S1-NTD) of the SARS-CoV-2 spike protein in comparison to the SARS-CoV in particular, and to other viruses presenting similar characteristic in general. Given the severity and the wide and rapid spread of the SARS-CoV-2 infection, it is very likely that the virus recognizes other receptors/co-receptors besides the ACE2. The NTD of the SARS-CoV-2 contains a receptor-binding motif different from that of SARS-CoV, with some insertions that could confer to the new coronavirus new receptor binding abilities. In particular, motifs similar to the insertion 72GTNGTKR78 have been found in structural proteins of other viruses; and these motifs were located in putative regions involved in recognizing protein and sugar receptors, suggesting therefore that similar binding abilities could be displayed by the SARS-CoV-2 S1-NTD. Moreover, concerning the origin of these NTD insertions, our findings point towards an evolutionary acquisition rather than the hypothesis of an engineered virus.