Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_{\nu}$, where $U_{e}$ and $U_{\nu}$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the predictions based on the sum rules which the Dirac phase $\delta$ present in $U$ satisfies when $U_{\nu}$ has a form dictated by, or associated with, discrete symmetries and $U_e$ has a ``minimal'' form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_{\nu}$, so that the reactor, atmospheric and solar neutrino mixing angles $\theta_{13}$, $\theta_{23}$ and $\theta_{12}$ have values compatible with the current data. We construct the likelihood function for $\cos \delta$, using i) the latest results of the global fit analysis of neutrino oscillation experiments and ii) the prospective sensitivities on the Pontecorvo, Maki, Nakagawa, Sakata (PMNS) mixing angles. Our results, in particular, show that the experimental measurement of the Dirac phase in the PMNS mixing matrix together with an improvement of the precision on the mixing angles can provide unique information about the possible symmetry in the lepton sector.