  In this paper we search for dynamical traversable wormhole solution in the
modified $f(T)$ theory of gravity, $T$ being the torsion scalar. For such
wormhole, the time dependence is inserted in the static traversable wormhole
metric of Morris and Thore. Two set of tetrads are adopted: the diagonal and
the non-diagonal tetrads. The diagonal set of tetrads constrains and reduces
$f(T)$ model to teleparallel theory where usual solutions have been found. With
diagonal set of tetrads, free from the teleparallel theory constraint, our
results show that the existence of traversable wormhole is possible only for
non-dynamical spacetime metric, i.e, static traversable wormhole solutions.
Moreover we take into account energy condition analysis and the results show
that the violation of NEC is not determinant for existence of static
traversable wormhole solutions.
