One of the main astrophysical processes leading to strong emission of gravitational waves to be detected by the future space-borne interferometer LISA is the capture of a compact star by a black hole with a mass of a few million solar masses in the center of a galaxy. In previous studies, main sequence stars were thought not to contribute because they suffer from early tidal disruption. Here we show that, according to our simulations of the stellar dynamics of the Sgr A^* cluster, there must be one to a few low-mass main sequence stars sufficiently bound to the central Galactic black hole to be conspicuous sources in LISA observations. The probability that a white dwarf may be detectable is lower than 0.5 and, in spite of mass segregation, detection of a captured neutron star or stellar black hole in the center of the Milky Way is highly unlikely.