The 22-year-old midfielder confirmed the La Liga giants were in talks with Ajax over his signature following Saturday's 2-2 Eredivisie draw against Vitesse - a match in which he scored and got an assist.
Van de Beek has emerged as a €60 million (£55m/$67) target for Real Madrid, who have been unable to pry French World Cup winner Paul Pogba from Manchester United.
Ajax - Champions League semi-finalists last season - will face Greece champions PAOK in Tuesday's opening leg of their third-round qualifier at Stadio Toumbas in Thessaloniki.
When asked about Van de Beek's future by reporters during the pre-match press conference, Ten Hag said: "He has come here and is going to play.
"He'll play next week too [in the second leg]."
Van de Beek has chosen not to force through a move to 13-time European champions, but did admit he knew of discussions between the two clubs about his services for the coming season.
He also understood that he could be Real Madrid's second choice to Pogba, but explained that people shouldn't always believe what comes out in the media.
"It is true that Madrid are in talks with Ajax, but I can't say any more," Van de Beek told Fox Sports following the result against Vitesse.
"My agent will have spoken with them. Real Madrid are a great club to play for, but Ajax are still a great club. We'll see what happens.
"I haven't heard it being talked about like that, but it could be true [that I'm second choice to Pogba].
"There's more to it than what’s in the newspapers, but you don't have to believe everything that is written.
"There's always a lot of nonsense. I don't have to tell you what is and isn't true, but again, I'm focusing on Saturday [Ajax's Eredivisie season opener vs Vitesse] and the rest is up to you guys."
Van de Beek made 57 appearances for Ajax last season, scoring 17 goals and supplying 13 assists as Erik ten Hag's men clinched an Eredivisie and KNVB Beker double and reached the semi-finals of the Champions League.