A self-consistent Green-function description of concentrated polymer solutions and dense polymeric melts is presented. The method, which applies to both uniform and nonuniform systems, is used in this work to calculate the static structure factor of a homogeneous fluid of Gaussian model chains. Limiting expressions are obtained analytically for large, intermediate, and small wave vectors. The results conform to the well-known and often used polymer reference interaction site model, and other polymeric Liquid-state theories. The advantages of the Green-function description are discussed in relation to other polymer density functional methods, with special reference to the problem of polymer crystallization.