The asymptotic behaviors of the integrated density of states $N(λ)$ of Schrödinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading terms of $N(λ)$ as $λ\downarrow-\infty$ coincide with that for a Poisson point process, which is known. Moreover, for some Gibbs point processes corresponding to pairwise interactions, the leading terms of $N(λ)$ as $λ\downarrow-\infty$ are determined, which are different from that for a Poisson point process.