  Partial decay widths of the $X(3940)$ are evaluated in the $^3P_0$ quark
model, assuming a charmonium scenario for its structure. In the study all model
parameters are predetermined by other reactions. The work reveals that it is
difficult to accommodate the $X(3940)$ with any $c\bar c$ meson state in the
picture of the potential quark model plus the $^3P_0$ quark dynamics.
