The Chelsea ace, 30, was axed by Antonio Conte for the Blues’ clash with Manchester United earlier this month after a bust-up.
United and Real have been linked with a move for the former PSG star, who has impressed since returning to the Premier League in the summer of 2016.
And according to Spanish transfer outlet Don Balon, Luiz has agreed a deal with Real.
Real president Florentino Perez and Zinedine Zidane are big admirers of Luiz and they want the Brazil international to partner Sergio Ramos at the Bernabeu.
Speaking about the chances of Chelsea ace Luiz joining Real in January or next summer, pundit Steve Nicol said: “It would be a miss for him, I don’t see how he would play.
Chelsea are back in action on Saturday when the Blues host Newcastle in the Premier League’s early kick-off.
However, Luiz could miss the clash with a knee injury.