Liquid crystal (LC) droplets dispersed in aqueous solution have emerged as an optical probe for sensing the adsorption and interaction of biological species at the LC/aqueous interface. In this paper, we modify the surface of 4-n-penty1-4'-cyanobiphenyl (SCB) LC droplets by the adsorption of positively charged poly(diallykiimethylammonium chloride) (PDADMAC) and poly-(ethylenirnine) (PEI) with different molecular weights at the 5CB/water interface. The PDADMAC and PEI-modified SCB droplets show a radial director configuration in aqueous solution with salt concentrations above 150 mM. The adsorption of negatively charged bovine serum albumin (BSA) on the positively charged PDADMAC and PEI-modified 5CB droplets through electrostatic interaction can induce the radial-to-bipolar configuration transition of the SCB inside the droplets. We find that the concentration of BSA required to induce the configuration transition increases linearly with the decrease of the molecular weight of PDAMAC and PEI. Our results highlight the capability of the director configuration of LC droplets as an optical probe for sensing the interaction between proteins and polyelectrolytes at the LC/aqueous interface.