On the same day it was reported Real have agreed a deal with Ajax, Van de Beek told Fox Sports (h/t Carlos Forjanes of AS) the interest was real before saying his focus remains in Amsterdam.
He said: "Yes, Real Madrid are interested in me. But you go really fast. I can't talk about what there is and isn't. Right now, I want to concentrate on Vitesse."
Ajax begin their 2019-20 Eredivisie title defence away to Vitesse Arnhem on Saturday.
Journalist Marcelo Bechler (h/t Fox Sports Asia) reported Ajax have accepted Real's offer for their playmaker, who has already agreed terms and could rubber-stamp his move in the coming days:
Van de Beek, 22, was one of Ajax's less talked about stars during last season's miraculous run to the UEFA Champions League semi-finals.
He came up with assists during their 3-3 group-stage draw against Bayern Munich and the 4-1 last-16 win over Real Madrid. The central midfielder followed up with match-deciding goals in wins against Juventus and Tottenham Hotspur in the quarter and semi-finals, respectively.
Frenkie de Jong and Matthijs de Ligt, the biggest names to emerge from Ajax's league- and cup-winning campaign, joined European titans Barcelona and Juventus, respectively, earlier this summer.
Van de Beek had an almost even spread of nine goals and 10 assists in the Eredivisie, with the latter statistic putting him in an elite bracket in his position, per WhoScored.com:
Manchester United star Paul Pogba has been linked with a move to the Santiago Bernabeu after failing to compete for the highest honours in his second United stint. Tottenham Hotspur's Christian Eriksen has also been touted as a midfield target, though Brazil legend Rivaldo recently told Betfair (h/t Goal) the club need neither Premier League player.
Luka Modric has entered the final year of his contract in Madrid and will turn 34 in September. Midfield partner Toni Kroos turns 30 in January, but his future seems secure considering he signed a new four-year deal in May.
BT Sport posted footage of Van de Beek's composed 1-0 winner in the Champions League semi-final first leg against Spurs (UK only):
Ajax have built a reputation for developing players from within their academy before selling for big profit. This summer has already been extremely lucrative after they secured €75 million fees for each of De Ligt and De Jong.
Mario de la Riva of AS recently provided quotes from Ajax technical director Marc Overmars, who said: "Ajax cannot keep its big stars for too long. If they want to leave and win things beyond here, we are not able to retain them."
Both Van de Beek and De Ligt have played their entire careers at Ajax and joined the club's academy as boys, while De Jong joined from Willem II—who reserved 10 percent of his future transfer—in 2015 for just €1.
De la Riva wrote that Ajax value Van de Beek at €60 million (£54.9 million), meaning the Dutch powerhouse looks set for another magnificent piece of profit if that sum has been met.