In this paper we investigate the possibility to perform direct positioning by retrieving information from the wavefront curvature. Despite such an approach has been considered in the past at microwave and acoustic frequencies using extremely large antennas, it is of interest to investigate its potential exploitation at mm-wave with practical size antennas in the context of next 5G systems. Thus, here we first consider a dedicated model to gather the source position information from the wavefront curvature for different array architectures, i.e., traditional and lens-based arrays, and successively we derive the maximum likelihood estimator to investigate the attainable performance. Results, obtained for different number of antennas, i.e., for different array apertures, confirm the possibility to achieve interesting positioning performance using a single antenna array with limited dimensions.