We investigate the dynamics of interstellar dust particles in moderately high resolution (512(3) grid points) simulations of forced compressible transonic turbulence including self-gravity of the gas. Turbulence is induced by stochastic compressive forcing which is delta-correlated in time. By considering the nearly Jeans-unstable case, where the scaling of the simulation is such that a statistical steady state without any irreversible collapses is obtained, we obtain a randomly varying potential, acting as a second stochastic forcing. We show that, in this setting, low-inertia grains follow the gas flow and cluster in much the same way as in a case of statistical steady-state turbulence without self-gravity. Large. high-inertia grains, however, are accelerated to much higher mean velocities in the presence of self-gravity. Grains of intermediate size also show an increased degree of clustering. We conclude that self-gravity effects can play an important role for aggregation/coagulation of dust even in a turbulent system which is not Jeans-unstable. In particular, the collision rate of large grains in the interstellar medium can be much higher than predicted by previous work.