Asymmetric metal-dielectric nanostructures are demonstrated superior optical properties arising from the combination of strong enhancement of near-fields and controllable scattering characteristics which originate from plasmonic and high-index dielectric components. Here, being inspired by the recent advances of the asymmetric hybrid nanoparticles fabrication [Dmitry Zuev, et al., Adv. Mater. 28, 3087 (2016)], we suggest and study numerically a novel type of hybrid dimer nanoantennas. The nanoantennas consist of asymmetric metal-dielectric (Au/Si) nanoparticles and allow tuning of the near-and far-field properties via laser induced reshaping of the metal part at the nanoscale. We demonstrate an ability to modification of the scattering properties, near-field distribution profilis, normalized local density of states, and radiation patterns of the nanoantenna upon the laser reshaping. The parameters used to investigate these effects correspond to experimentally demonstrated values.