An earlier integral equation approach to percolation in macromolecular fluids is extended to include attractive interactions between the sites representing flexible polymers. An analytic treatment based on the threadlike chain model shows that the percolation threshold near the theta temperature is closely related to the usual semidilute overlap concentration, and is significantly below the value found under athermal conditions. These results are consistent with the findings of numerical calculations on tangent-bead chain models. The location of the static percolation threshold in the density-concentration plane with relation to the liquid-vapor spinodal boundary is investigated. Numerically obtained results for the percolation thresholds for both flexible and rigid athermal, finite thickness, macromolecules are presented, which are consistent with prior findings based on the analytically tractable threadlike chain model.