The Spanish youth international is set to sign a new contract at the Bernabeu which will insert a £9.6m minimum fee release clause. The La Liga champions are thought to be keen to discourage Arsenal from poaching the youngster, as reports have linked the Gunners with a move for the teenage midfielder.
Rodriguez reportedly rejected the offer of a five-year contract at Arsenal in October 2011, preferring instead to further his footballing education at Real Madrid, but the rebuttal has not put off Gunners boss Arsene Wenger.
Jose Mourinho is believed to be a huge fan of the young star, who has played 156 minutes for the Real Madrid first-team, and is ready to reward him with a new long-term contract when he turns 18 on December 16.
Madrid have been stung in the past by clubs nabbing their best young talent and developing them into top players.
Chelsea star Juan Mata left Madrid for Valencia in 2007, and has gone on to become a World Cup winner with Spain and a European champion with Chelsea.
The Bernabeu-based side also lost Roberto Soldado to Getafe in 2008, and are keen to avoid a repeat this time around.
Arsenal are thought to be ready to spend when the transfer window opens in January - Wenger has been linked with a move for a new striker - but it seems Rodriguez will not be arriving at the Emirates Stadium.