Context. At present, near-Earth objects (NEOs) are being discovered at an ever-increasing rate. However, their physical characterisation is still significantly lagging behind. In particular, the taxonomic classification of newly discovered NEOs is of great importance with regard to improving our understanding of the population of NEOs. Aims. In this context, our goal is to probe potential links between orbital properties of NEOs and their composition. We investigate whether we can make a reasonable guess about the taxonomic class of an NEO upon its discovery with a decent orbital accuracy. Methods. We used a G-mode multivariate statistical clustering method to find homogeneous clusters in a dataset composed of orbital elements of NEOs. We adopted two approaches, using two sets of variables as inputs to the G-mode method. In each approach, we analysed the available taxonomic distribution of resulting clusters to find potential correlations with several unique parameters that distinctively characterise NEOs. We then applied a dynamical model on the same clusters to trace their escape regions. Results. Approach 1 (A1) led us to obtain NEO clusters that can be linked to a primitive composition. This result was further strengthened by the dynamical model, which mapped outer-belt sources as escape regions for these clusters. We remark on the finding of a cluster akin to S-type NEOs in highly eccentric orbits during the same approach (A1). Two clusters, one with small NEOs in terrestriallike orbits and one with relatively high inclinations, were found to be common to both approaches. Approach 2 (A2) revealed three clusters that are only separable by their arguments of perihelion. Taken altogether, they make up the majority of known Atira asteroids. Conclusions. For an NEO whose orbit is relatively well determined, we propose a model to determine whether the taxonomy of an NEO is siliceous or primitive if the orbital elements of the NEO fall within the presented combinations of inclination, eccentricity, and semi-major axis ranges.