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 at least value 