De Jong's value was estimated at £50m (€56m) when rumours of United interest surfaced earlier this month, rivalling Barcelona and Tottenham, both of whom are believed to have been tracking the 21-year-old for some time.
According to a report from Dutch publication De Telegraaf, Real have identified De Jong as a long-term successor to 33-year-old newly crowned 2018 Best FIFA Men's Player Luka Modric.
According to Dutch daily De Telegraaf, Real Madrid are willing to pay € 80 million for Ajax midfielder Frenkie de Jong. Manchester United are also interested (supposedly United's scouts have already visited Ajax games) pic.twitter.com/gn0dVL63r0— Elko Born (@Elko_B) September 24, 2018
The reigning European champions are said to be willing to offer €80m (£72m) to strike a deal. The possibility of a bidding war between several of Europe's biggest clubs will no doubt come as good news to Ajax, who managed to keep hold of De Jong this summer.
De Telegraaf notes that Paris Saint-Germain, Bayern Munich and Manchester City have also been showing interest in De Jong, with last week's Champions League display for Ajax against AEK Athens enough to convince Manchester United and Real Madrid that he is the real deal.
When pressed on transfer links by the newspaper, De Jong's agent Ali Dursun refused to give anything away and referred all questioning to Ajax director Marc Overmars.
"I can neither confirm nor deny [interest from Manchester United and Real Madrid]. You have to ask Marc Overmars because I send all the clubs that report to me to him," Dursun said.