  Inspired by the LHCb's observations of hidden-charm $P_{c(s)}$ states, we
study their hidden-strange analogues $P_s$ states in both $[udu][\bar ss]$ and
$[uds][\bar su]$ configurations. We investigate the $P_s$ pentaquark states in
$p\eta^\prime$, $p\phi$, $\Lambda K$, $\Sigma K$ and $\Sigma^\ast K^\ast$
structures with $J^P = \frac{1}{2}^-$ and $\Sigma ^\ast K$ and $\Sigma K^\ast$
with $J^P = \frac{3}{2}^-$, and calculate their masses in the framework of QCD
sum rules. Our numerical results show that the extracted hadron masses for all
the $p\eta^\prime$, $p\phi$, $\Lambda K$, $\Sigma K$ and $\Sigma^\ast K^\ast$
structures are much higher than $\Sigma K$ mass threshold and masses for
$\Sigma ^\ast K$ and $\Sigma K^\ast$ also higher than threshold of
corresponding hadron, so that no bound state exists in such channels, which is
consistent with the experimental status to date.
