We study the morphologies of nematic nanodrops in a vapor of a discotic nematogen by Monte Carlo simulations. The fluid interactions are modeled by a Gay-Berne model with molecular elongations of κ = 0.3 and 0.5 and different values of the energy anisotropy parameter κ' in the range of temperature T in which the nematic coexists with a vapor phase. We considered nanodrops of N = 4000 and 32 000 particles. For κ > κ', we observe that nanodrops are quite spherical (even for N = 4000 nanodrops), with a homogeneous director field for κ = 0.3 and a bipolar nematic configuration with tangential anchoring for κ = 0.5. By increasing the value of κ', nanodrops change from spherical to lens-shaped for κ = 0.3, and for κ = 0.5, spherical nanodrops with homeotropic anchoring and a disclination ring located on its equatorial plane are observed. Although no radial nanodrops are observed, isotropic liquid nanodrops with a paranematic shell and radial texture are observed for temperatures slightly above the vapor-isotropic-nematic triple point when the vapor-isotropic interface is completely wet by the nematic phase.