The formation of complexes between nanoparticles and polyelectrolytes is a key process for the control of the reactivity of manufactured nanoparticles and rational design of core shell nanostructures. In this work, we investigate the influence of the nanoparticle dielectric constant on the adsorption of a linear charged polymer polyelectrolytes at the surface of a neutral nanoparticle. The polyelectrolyte linear charge density, as well as the image charges in the nanoparticle due to the dielectric discontinuity, is taken into account. Monte Carlo simulations are used to predict the adsorption/desorption limits and system properties. Effects of the nanoparticle size and polyelectrolyte length are also investigated. The polyelectrolyte is found adsorbed on the nanoparticle when the dielectric constant of the nanoparticle is greater than the dielectric constant of the medium. Attractive interactions induced by the presence of opposite sign image charges are found strong enough to adsorb the polyelectrolyte showing that the reaction field contribution has to be considered. The affinity between the polyelectrolyte and the nanoparticle is found to increase in magnitude by increasing the nanoparticle size and dielectric constant. The reaction field magnitude is also found to depend in a nonlinear way from the polyelectrolyte length.