© 2020 American Physical SocietyAdvanced gravitational-wave detectors are limited by quantum noise in their most sensitive frequency band. Quantum noise suppression techniques, such as the application of the quantum squeezed state of light, have been actively studied in the context of homodyne readouts. In this paper, we consider quantum squeezing schemes for the heterodyne readouts. This is motivated by a successful suppression of the higher-order-mode content by stable recycling cavities in advanced detectors. The heterodyne readout scheme requires precise tuning of the interferometer parameters and a broadband squeezing source, but is conceptually simple and elegant. We further show that it is compatible with the frequency-dependent squeezing, which reduces both the shot noise and the radiation-pressure noise. We propose a test of the heterodyne readout with squeezing in Advanced LIGO. This can serve as a pathfinder not only for the implementation in future detectors, such as the Einstein Telescope and Cosmic Explorer, but also for general high-precision optical measurements.