Barca had an offer for De Jong turned down over the summer, with Ajax chief Marc Overmars stating this week the Catalans' proposal fell well short of their valuation.
Barca, however, remain keen - but will face competition from Real.
Okdiario's chief pundit Eduardo Inda, speaking on El Chiringuito, revealed: "He is the great star of Dutch football. Madrid is certainly interested. If they can, they will sign him."
Real rate De Jong highly and believe he can cover the positions of "Casemiro, (Toni) Kroos and (Luka) Modric".
While Ajax turned down a €50m offer from Tottenham for De Jong, Real are prepared to offer €80m in January for the newly-capped Holland international.