The 17-year-old has played just 156 minutes of football for Madrid’s first team, but it is believed Jose Mourinho has high hopes for the player and is looking to tie him down to a new contract once he turns 18 on December 16th.
The contract will contain a substantial release clause of £9.6million which they will continue to increase in a bid to deflect away interest in the player from other clubs, with Arsenal boss Arsene Wenger said to be one of his keenest admirers.
Real want to avoid a repeat of when they lost Juan Mata to Valencia in 2007, the Spanish international who of course has gone on to light up the Premier League with Chelsea.
Roberto Soldado was another player that got away when he left for Getafe in 2008, and he is now a prolific goalscorer for Valencia which has earned him a place in the Spanish international squad.
Rodriguez who plays as a central midfielder has previously turned down a five-year contract offer from Arsenal in October 2011, but it is believed that he is still a target for the the Gunners boss.