Prewetting transitions in polymer blends near a hard surface which favors one of the phases in the blend are studied by both mean-held and Monte Carlo methods. The mean-field results predict for systems that have a first-order wetting transition at a bulk density of (rho(infinity))(W), there exists first-order prewetting transitions for (rho(infinity))(W) less than or equal to rho(infinity)<(rho(infinity))(PW). For rho(infinity)>(rho(infinity))(PW) there exist second-order transitions so that (rho(infinity))(PW) may be identified as the prewetting critical point. Monte Carlo simulations of the bond fluctuation model on a simple cubic lattice between two hard walls H lattice spacings apart are performed and qualitative agreement is found with the mean-field predictions.