We numerically demonstrate that properly designed plasmonic covers can be used to enhance the performance of near-field scanning optical microscopy (NSOM) systems based on the employment of apertureless metallic tip probes. The covering material, exhibiting a near-zero value of the real permittivity at the working frequency, is designed in such a way to dramatically reduce the undesired scattering due to the strongly plasmonic behavior of the tip. Though the light scattering by the tip end is necessary for the correct operation of NSOMs, the additional scattering due to the whole probe affects the signal-to-noise ratio and thus the resolution of the acquired image. By covering the whole probe but not the very tip, we show that unwanted scattering can be effectively reduced. A realistic setup, working at mid-IR frequencies and employing silicon carbide covers, has been designed and simulated to confirm the effectiveness of the proposed approach.