Isco, 21, has long been linked with Madrid as well as Manchester City but the arrival of new Real coach Carlo Ancelotti, who was unveiled as the successor to Jose Mourinho on Wednesday, appears to have accelerated the transfer.
Spanish newspaper AS quoted Perez telling Radio Nacional: "There is an agreement with the club and the player. He will be presented next week after the medical."
Reports in Spain suggest the fee will be in the region of 27million euros.
Isco recently starred as Spain's Under-21 team retained the European Championship, scoring three times in their successful campaign in Israel.
Ancelotti was asked about the former Valencia man at his press conference.
The Italian said: "From what I have seen of him, it's clear he has a lot of quality.
"Spain's Under-21 side has a lot of great players and he is one of the best.
"He could get into any team in the world, so he could also play for Madrid."
Isco would be Madrid's second acquisition of the summer after they re-signed full-back Dani Carvajal on a buy-back deal from Bayer Leverkusen.
- Sports & Recreation
- Carlo Ancelotti
- Jose Mourinho