  In this paper we study the possibility of having a wormhole (WH) as a
candidate for the Sgr A$^\star$ central object and test this idea by
constraining their geometry using the motion of S2 star and the reconstructed
shadow images. In particular, we consider three WH models, including WHs in
Einstein theory, brane-world gravity, and Einstein-Dirac-Maxwell theory. To
this end, we have constrained the WH throat using the motion of S2 star and
shown that the flare out condition is satisfied. We also consider the accretion
of infalling gas model and study the accretion rate and the intensity of the
electromagnetic radiation as well as the shadow images.
