Optical nanoantennas, especially of the dipole type, have been theoretically and experimentally demonstrated by many research groups. Likewise, the plasmonic waveguides and optical circuits have experienced significant advances. In radio frequencies and microwaves a category of antenna known as dielectric resonator antenna (DRA), whose radiant element is a dielectric resonator (DR), has been designed for several applications, including satellite and radar systems. In this letter, we explore the possibilities and advantages to design nano DRAs (NDRAs), i. e., DRAs for nanophotonics applications. Numerical demonstrations showing the fundamental antenna parameters for a circular cylindrical NDRA type have been carried out for the short (S), conventional (C), and long (L) bands of the optical communication spectrum.