Hypothetical exomoons around close-in giant planets may migrate inwards and/or outwards in virtue of the interplay of the star, planet and moon tidal interactions. These processes could be responsible for the disruption of lunar systems, the collision of moons with planets or could provide a mechanism for the formation of exorings. Several models have been developed to determine the fate of exomoons when subject to the tidal effects of their host planet. None of them have taken into account the key role that planetary evolution could play in this process. In this paper we put together numerical models of exomoon tidal-induced orbital evolution, results of planetary evolution and interior structure models, to study the final fate of exomoons around evolving close-in gas giants. We have found that planetary evolution significantly affects not only the time-scale of exomoon migration but also its final fate. Thus, if any change in planetary radius, internal mass distribution and rotation occurs in time-scales lower or comparable to orbital evolution, exomoon may only migrate outwards and prevent tidal disruption or a collision with the planet. If exomoons are discovered in the future around close-in giant planets, our results may contribute to constraint planetary evolution and internal structure models.