It is known that the adsorption of surfactants at the liquid crystal (LC)/aqueous interface can induce a bipolar-to-radial director configuration of LC droplets dispersed in aqueous solution. In this paper, we study the effect of charged polyelectrolyte-coating on the interaction of surfactants and LC droplet cores by observing the director configuration of the LC droplet cores as a function of surfactant concentrations. It is found that surfactants can penetrate into the polyelectrolyte coating and react with the LC droplet cores to induce the bipolar-to-radial transition of the LC inside the droplet cores. However, the concentration of charged surfactants required to induce the configuration transition of the LC droplet cores is affected by the charged polyelectrolyte coating. The effect is significantly enlarged with decreasing the alkyl chain length of charged surfactants. Our results highlight the possibility of engineering polyelectrolyte coatings to tune the interaction of LC droplets with analysts, which is critical towards designing LC droplet based sensors.