We present near-field measurements of optical Yagi-Uda nanoantennas that are used in receiving mode. The eigenmode imaging of amplitude and phase by apertureless scanning near-field optical microscopy allows us to investigate the dynamics of the local out-of-plane electric field components and to visualize the temporal evolution of this time-harmonic reception process. The antenna directionality manifests itself by the dependence of the local field enhancement at the feed element on the illumination direction. Simulations taking into account the substrate confirm our observation of the directionality. Our work demonstrates the possibility to characterize multielement nanoantennas by electromagnetic antenna near-field scanners.