A discretized version of the polymer-reference interaction site model (RISM) theory is investigated on its capabilities to assess the adsorption behavior of interacting polymeric lattice fluids near a flat wall. Both the density profile of the fluid at the wall and the equation of state of the bulk fluid (obtained from the density profile via a method of Dickman) are compared to Monte Carlo simulations. The profiles are also compared to the outcome of a classical lattice-based adsorption theory, the Scheutjens-Fleer formalism. At all bulk packing fractions, the Scheutjens-Fleer theory is found to be superior to the polymer-RISM theory, although it is made plausible that the performance of the discretized polymer-RISM theory can be improved significantly by using a nonreversal random walk intramolecular distribution, instead of the random walk intramolecular distribution used in this work.