"The whites and Malaga reached an agreement in principle for the player yesterday (Friday)," said Madrid sports daily AS.
"With just a few final details of the playmaker's contract to be finished, he will be a Madrid player for the next five seasons.
"The agreement will be made official next week with the player to be presented at the start of July."
Isco was Malaga's shining light with three goals as the Andalusians reached the Champions League quarter-finals in their first ever participation in the competition and was also on target three times as Spain retained their U-21 Euros tile in Israel earlier this month.
The former Valencia man also admitted last week to already having received offers from Madrid and Manchester City, where he could have rejoined former Malaga boss Manuel Pellegrini.
However, the player's first choice was always thought to be Madrid and the recommendation of Zinedine Zidane seems to have convinced Real president Florentino Perez to make the playmaker his first big signing of the summer.