The common envelope phase is a likely formation channel for close binary systems containing compact objects. Neutron stars in common envelopes accrete at a fraction of the Bondi-Hoyle-Lyttleton accretion rate, since the stellar envelope is inhomogeneous, but may still be able to accrete at hyper-critical rates (though not enough to become black holes). We show that common envelope systems consisting of a neutron star with a massive primary may be gravitational wave sources detectable in the Advanced LIGO band as far away as the Magellanic Clouds. From the range of possible accretion rates relevant to common envelope evolution, we find that these systems may be significantly louder gravitational wave sources than low-mass X-ray binaries like Sco X-1, which are currently the target of directed searches for continuous GWs. We also find that their strain amplitude signal may allow for novel constraints on the orbital separation and inspiral timescale in common envelopes when combined with pre-common envelope electromagnetic observations.