By extending a recently developed Bethe lattice theory, we calculate the cluster size distribution and average cluster size of voids in the presence of polymers. Because of the presence of interactions and because polymers have a size different from that of voids, the model we investigate is a correlated percolation model. The effects of interactions, the pressure P, the degree of polymerization (DP) M, the coordination number q, and the possibility of void percolation on the above properties are evaluated. It is found that small-sized clusters are in overwhelming majority and constitute a large fraction of the total free volume in cases of interest. Attractive monomer-monomer interactions favor the formation of larger clusters. As a function of the DP, the average cluster size shows very different behavior in two regions: with void percolation and without void percolation. The following results are valid at constant temperature and pressure. In the presence of percolation, the average cluster size increases with M, whereas in the absence of percolation it decreases with M. In the absence of void percolation, the average cluster size decreases with increasing q due to the decrease in the total free volume. We present and discuss the results and compare them with those from experiments, simulations and random percolation. We conclude that we are able to qualitatively explain experimental results if we assume that there is no void percolation.