The Manchester City midfielder comes off contract in June and can join Real in June on a Bosman transfer.
However, AS says Perez doesn't want to wait and is keen to bring Diaz to Madrid in January.
And all parties involved are in agreement. Diaz doesn't want to stay with City for another six months, while the Premier League champs would be happy to rake in a fee for a player they otherwise would lose for nothing.
City would seek €5-10m to sell Diaz to Real Madrid next month.