The 26-year-old has only made 15 appearances for his Turkish club during the 2019-20 campaign having picked up a serious knee injury in November.
Aston Villa were strongly linked with the Congo international ahead of the January transfer window, although the centre-back's injury ended any chance of him leaving at the start of 2020.
According to Takvim, Galatasaray are open to offers for a number of players this summer as they look to raise some funds, and Luyindama could be made available for transfer.
The report claims that West Ham are keeping a close eye on developments and could launch a €15m (£14m) offer during this summer's transfer window.
Luyindama will see his current deal in Turkey expire at the end of the 2021-22 season.