  A near-threshold enhancement in the $D_s^+ D_s^-$ system, dubbed as
$X(3960)$, is observed by the LHCb collaboration recently. A combined analysis
on $\chi_{c0}(3930)~(\to D^+ D^-)$, $X(3960)~(\to D_s^+ D_s^-)$, and
$X(3915)~(\to J/\psi\omega)$ is performed using both a $K$-matrix approach of
$D_{(s)}\bar{D}_{(s)}$ four-point contact interactions and a model of
Flatt\'e-like parameterizations. The use of the pole counting rule and spectral
density function sum rule indicate, under current statistics, that this $D_s^+
D_s^-$ near-threshold state has probably the mixed nature of a $c\bar{c}$
confining state and $D_s^+ D_s^-$ continuum.
