Wetting by a polymer fluid at an attractive surface is investigated using density functional theory. It is shown that the qualitative behavior of the wetting temperature, T-w, as a function of the polymer length, depends on the strength of the surface potential. Defining T-c as the bulk critical temperature, we find that the normalized wetting temperature, T-w/T-c, shows nonmonotonic dependence on polymer length. For weak surface potentials, T-w/T-c increases with polymer length and, in some cases, wetting seems to be suppressed. It is conjectured that this may occur via an encroaching drying transition.