  Motivated by the continuous experimental investigations of $X(1835)$ in
three-body decay channels like $\eta^\prime \pi^+ \pi^-$, we investigate the
$\eta^\prime K \bar K$ system with the aim of searching for bound states and/or
resonances when the dynamics involved in the $K\bar K$ subsystem can form the
resonances: $f_0(980)$ in isospin 0 or $a_0(980)$ in isospin 1. For this, we
solve the Faddeev equations for the three-body system. The input two-body
$t$-matrices are obtained by solving Bethe-Salpeter equations in a coupled
channel formalism. As a result, no signal of a three-body bound state or
resonance is found.
