  We apply the method of QCD sum rules to study the $s s \bar s \bar s$
tetraquark states of $J^{PC} = 0^{-+}$. We construct all the relevant $s s \bar
s \bar s$ tetraquark currents, and find that there are only two independent
ones. We use them to further construct two weakly-correlated mixed currents.
One of them leads to reliable QCD sum rule results and the mass is extracted to
be $2.51^{+0.15}_{-0.12}$ GeV, suggesting that the $X(2370)$ or the $X(2500)$
can be explained as the $ss\bar s\bar s$ tetraquark state of $J^{PC} = 0^{-+}$.
To verify this interpretation, we propose to further study the $\pi\pi/K \bar
K$ invariant mass spectra of the $J/\psi \to \gamma \pi \pi \eta^\prime/\gamma
K \bar K \eta^\prime$ decays in BESIII to examine whether there exists the
$f_0(980)$ resonance.
