We design an integrated optoelectronic device based on the whispering-gallery modes of a sapphire microsphere integrated with a liquid-crystal tuning medium to produce a narrowband, electrically tunable, channel-dropping filter. The sapphire microsphere is glued over a diffused waveguide in a glass substrate. At the base of the microsphere, a small volume of liquid crystal is infiltrated. We numerically evaluate the performance of the device and demonstrate a voltage tuning of the narrowband resonances.