Already highly fancied and constantly linked with Barcelona over the summer, De Jong has now attracted the gaze of the European Champions, as well as Tottenham.
However, as has been the case for a while, Ajax are insisting their star is not for sale at any cost.
'Mundo Deportivo' reported earlier in the summer that Spurs had a bid of €50m turned down by the Amsterdam side, but Real Madrid normally have a way of getting what they want.
Liverpool midfielder Gini Wijnaldum was full of praise for De Jong after he made his Holland debut: "Frenkie is a great player, he did a good job and makes it easier for us by the way he plays football.
"A lot has been written about him lately, so I've been watching how he plays at Ajax. He is doing very well now, but we have often had Dutch players who first played very well then later became less."