  The observation of neutrino oscillation as well as the recent experimental
result on lepton flavor universality (LFU) violation in $B$ meson decays are
indications of new physics beyond the Standard Model. Many theoretical models,
which are introduced in the literature as an extension of SM to explain these
observed deviations in LFU, lead to new kind of interactions so-called
non-standard interaction (NSI) between the elementary particles. In this paper,
we consider a model with an additional $Z'$ boson (which is quite successful in
explaining the observed LFU anomalies) and analyze its effect in the lepton
flavour violating (LFV) $B_d\to \tau^\pm e^\mp$ decay modes. From the present
upper bound of the $B_d\to \tau^\pm e^\mp$ branching ratio, we obtain the
constraints on the new physics parameters, which are related to the
corresponding NSI parameters in the neutrino sector by $SU(2)_L$ symmetry.
These new parameters are expected to have potential implications in the
neutrino oscillation studies and in this work we investigate the possibility of
observing the effects of these interactions in the currently running and
upcoming long-baseline experiments, i.e., NOvA and DUNE respectively.
