Calculation of gravitational radiation during binary spiralling-in leading to the possible formation of a Thorne-Zytkow (TZ) object (a neutron star inside a supergiant core) is performed. The calculations were done for polytropic density distributions with different indices n, as well as for realistic models of supergiants. A maximum frequency of the emitted gravitational waves during this process was found to range from a few to 300 initial keplerian orbital frequencies, that is from 10^-5^ to ~0.1Hz, depending on the model. The dimensionless strain metric amplitude can reach h~10^-23.5^ for a source lying 10kpc away from the Sun. We conclude that TZ objects forming at a rate of 1 per 500 yrs in the Galaxy could be potential astrophysical targets for space laser intereferometers. Analysis of gravitational waveforms emitted during TZ-object formation could bring a unique information about stellar structure.