  In this work we study the $D^* \bar{D}^*$ current with QCD sum rules. We
write the correlation function using the general current corresponding to the
$D^* \bar{D}^*$ system and then use spin projectors to obtain the correlation
function in the $0^+, 1^+$ and $2^+$ spin-parity configurations. The purpose of
the present work is to investigate the possibility of explaining the recently
reported $Z_c(4025)$ as a $D^* \bar{D}^*$ moleculelike state. As a result we
find a state for each spin case with a very similar mass: $M^{S=0} = \left(3943
\pm 104\right)$ MeV, $M^{S=1} = \left(3950 \pm 105\right)$ MeV, $M^{S=2} =
\left(3946 \pm 104 \right)$ MeV. We discuss that our mass results, within error
bars, for $1^+$ or $2^+$ are both compatible with $Z_c(4025)$. However, our
results are also compatible with a possible $D^* \bar{D}^*$ bound state, in
agreement with predictions of some previous works. We have also calculated the
current-state coupling which turns out to be larger in the $2^+$ case.
