We propose the design of switchable plasmonic nanoantennas (SPNs) that can be employed for optical switching in the near-infrared regime. The proposed SPNs consist of nanoantenna structures made up of a plasmonic metal (gold) such that these nanoantennas are filled with a switchable material (vanadium dioxide). We compare the results of these SPNs with inverted SPN structures that consist of gold nanoantenna structures surrounded by a layer of vanadium dioxide (VO) on their outer surface. These nanoantennas demonstrate switching of electric-field intensity enhancement (EFIE) between two states (On and Off states), which can be induced thermally, optically or electrically. The On and Off states of the nanoantennas correspond to the metallic and semiconductor states, respectively of the VO film inside or around the nanoantennas, as the VO film exhibits phase transition from its semiconductor state to the metallic state upon application of thermal, optical, or electrical energy. We employ finite-difference time-domain (FDTD) simulations to demonstrate switching in the EFIE for four different SPN geometries - nanorod-dipole, bowtie, planar trapezoidal toothed log-periodic, and rod-disk - and compare their near-field distributions for the On and Off states of the SPNs. We also demonstrate that the resonance wavelength of the EFIE spectra gets substantially modified when these SPNs switch between the two states.