An academy product of the German side, the centre-back played a vital role in helping Schalke climb out of the second division last season.
The centre-back made 31 appearances in the league and helped Schalke’s promotion bid, with his performances seeing him linked with Celtic.
Celtic were reported to be interested in bringing the centre-back to Parkhead and he was even claimed to be in talks with them.
However, it is suggested that such talk is wide of the mark and Celtic are not pushing to take the player to Scotland.
The Celts are in the centre-back market but it will not be Thiaw who will fill the gap for the Scottish champions next season.
Celtic were also interested in another centre-back who played for Schalke last season, Ko Itakura, and with his proposed move to Borussia Monchengladbach halted, the Hoops could still have a chance to sign him.
Meanwhile, a centre-back is set to head the other way as Celtic’s Christopher Jullien is nearing an exit to Schalke.
