  We classify all possible texture zeros in light neutrino mass matrix in
diagonal charged lepton basis by considering Dirac nature of light neutrinos.
For Hermitian nature of neutrino mass matrix, the number of possible texture
zeros remain same as Majorana texture zeros, but with less free parameters due
to the absence of additional Majorana CP phases. Relaxing the Hermitian nature
of neutrino mass matrix lead to many more possibilities and freedom due to
additional CP phases, mixing angles not constrained by neutrino data. While we
find that none of the texture zeros in Hermitian case are allowed, in
non-Hermitian case some textures even with four zeros are allowed. While most
of the one-zero, two-zero and three-zero textures in this case are allowed,
four-zero textures are tightly constrained with only 6 allowed out of 126
possibilities. The allowed textures also give interesting correlations between
light neutrino parameters with sharp distinctions between normal and inverted
mass ordering. Many of these allowed textures also saturate the Planck 2018
upper bound on the sum of absolute neutrino masses.
