Van De Beek recently told Fox Sports (h/t Carlos Forjanes of AS) the Spanish giants were "interested in me."
Ten Hag, though, is confident that Van De Beek is committed to Ajax and could stay past the end of the transfer window at the beginning of September, per Marca:
"[Van de Beek] only dedicates himself to playing. I guess and I hope that he stays with us this season. Otherwise, I will hear from [Ajax director of football] Marc Overmars."
Ajax have lost a number of key players this summer from the squad that won the Dutch league title last season and made it to the semi-finals of the UEFA Champions League, knocking out Real Madrid and Juventus on the way.
Most notably, midfielder Frenkie de Jong has gone to Barcelona and centre-back Matthijs de Ligt has joined Juventus:
If Van De Beek were to leave also, it would be a big blow for Ajax, as he is superb on the ball, boasts a fantastic passing range and is only likely to get better with more experience.
The Dutchman netted nine goals and provided 10 assists in the Dutch top flight last season, and he has started the new campaign in brilliant fashion, already registering two goals and two assists in two appearances:
Real are fairly ruthless, though, when it comes to signing the targets they want.
They look to have missed out on Pogba and Tottenham Hotspur's Christian Eriksen in their bid to strengthen in the midfield.
But should Los Blancos decide that they cannot go into the 2019-20 season without strengthening in the middle of the park, they have the financial clout to table tempting offers to both Ajax and Van De Beek.