  In this work we explore the possible existence of static, spherically
symmetric and stationary, axisymmetric traversable wormholes coupled to
nonlinear electrodynamics. Considering static and spherically symmetric (2+1)
and (3+1)-dimensional wormhole spacetimes, we verify the presence of an event
horizon and the non-violation of the null energy condition at the throat. For
the former spacetime, the principle of finiteness is imposed, in order to
obtain regular physical fields at the throat. Next, we analyze the
(2+1)-dimensional stationary and axisymmetric wormhole, and also verify the
presence of an event horizon, rendering the geometry non-traversable.
Relatively to the (3+1)-dimensional stationary and axisymmetric wormhole
geometry, we find that the field equations impose specific conditions that are
incompatible with the properties of wormholes. Thus, we prove the non-existence
of the general class of traversable wormhole solutions, outlined above, within
the context of nonlinear electrodynamics.
