  The recent finding of the gravitational wave (GW) signal by the NANOGrav
collaboration in the nHZ frequency range has opened up the door for the
existence of stochastic GWs. In the present work, we have argued that in a hot
dense neutrino asymmetric plasma, GWs could be generated due to the instability
caused by the finite difference in the number densities of the different
species of the neutrinos. The generated GWs have amplitude and frequency in the
sensitivity range of the NANOGrav observation. We have shown that the GWs
generated by this mechanism could be one of the possible explanations for the
observed NANOGrav signal. We have also discussed generation of GWs in an
inhomogeneous cosmological neutrino plasma, where GWs are generated when
neutrinos enter a free streaming regime. We show that the generated GWs in an
inhomogeneous neutrino plasma cannot explain the observed NANOGrav signal. We
have also calculated the lower bound on magnetic fields' strength using the
NANOGrav signal and found that to explain the signal, the magnetic fields'
strength should have atleast value $\sim 10^{-12}$ G at an Mpc length scale.
