A central defender is top of los Merengues' list for their summer rebuilding plans and the powerful Brazilian is the number one target.
Madrid's sporting director, Predrag Mijatovic, wants Alex for his pace and strength to complement Sergio Ramos and Fabio Cannavaro.
Chelsea have said that they are taking the 25-year-old back after he has spent the last three seasons on loan at PSV Eindhoven and will use him in their first-team.
That announcement has not stopped Madrid from making their interest known and, according to reports in Spain, the player would prefer la Primera to the Premiership.
Mijatovic has maintained contact with Alex's agent, Giuliano Bertolucci, but after the Blues hard work to earn the player a work permit they are unlikely to listen to any offers.
Should interest in Alex hit a wall, Madrid have also made their interest in Roma's Romanian central defender, Cristian Chivu, known.
The former Ajax star has already held talks with Inter and FC Barcelona and is expected to choose between those two clubs, leaving Madrid to look further afield.
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Madrid failed to lure players despite winning the Primera Liga while Barce signed Henry and Toure.