We re-evaluate the outer edge of orbital stability for possible exomoons orbiting the radial velocity planet discovered in the HD 23079 system. In this system, a solar-type star hosts a Jupiter-mass planet in a nearly circular orbit in the outer stellar habitable zone. The outer stability limit of exomoons is deduced using N-body and tidal migration simulations considering a large range of initial conditions, encompassing both prograde and retrograde orbits. In particular, we extend previous works by evaluating many values in the satellite mean anomaly to identify and exclude regions of quasi-stability. Future observations of this system can make use of our results through a scale factor relative to the currently measured minimum mass. Using a constant time lag tidal model (Hut 1981), we find that plausible tidal interactions within the system are insufficient to induce significant outward migration toward the theoretical stability limit. While current technologies are incapable of detecting exomoons in this system, we comment on the detectability of putative moons through Doppler monitoring within direct imaging observations in view of future research capacities.