The extreme conditions of pressure and energy density at the cores of neutron stars can be a valuable asset in the investigation of high energy physics processes. Asymptotic freedom of quarks also makes the formation of a quark-gluon plasma core a viable hypothesis. Such hybrid stars, containing a core of quark matter surrounded by a mantle of neutron rich nuclear matter, might present a density discontinuity at the interface of those phases, which can generate g-modes detectable via gravitational wave observations. This work aims to calculate the eigenfrequencies of these g-modes for various hybrid stars compositions using numerical methods, and discuss their detectability by current and next generation GW observatories such as the Advanced LIGO-Virgo and the Einstein Telescope.