  The cosmological model of the modified Chaplygin gas interacting with cold
dark matter is studied. Our attention is focused on the final state of universe
in the model. It turns out that there exists a stable scaling solution, which
provides the possibility to alleviate the coincidence problem. In addition, we
investigate the effect of the coupling constants $c_{1}$ and $c_{2}$ on the
dynamical evolution of this model from the statefinder viewpoint. It is found
that the coupling constants play a significant role during the dynamical
evolution of the interacting MCG model. Furthermore, we can distinguish this
interacting model from other dark energy models in the $s-r$ plane.
