The 39-year-old hails his former colleague, saying that it was a "privilege" to work with the now-Chelsea boss after Carlo Ancelotti was officially named as his successor
The newly appointed Chelsea boss endured a turbulent final year at the Santiago Bernabeu, reportedly falling out with a number of players towards the end of his three-year spell in the Spanish capital.
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Karanka told DTLux Magazine: "I was the person who knew Mourinho better than anybody else and I have to say that it was a privilege to work with him.
"I am proud to be able to say I am a friend of his. It was my first experience in the coaching field, and it was an incredible experience with him."
Mourinho chose the 39-year-old as his assistant upon taking the reins at the Bernabeu in 2010 and Karanka often deputised for the former Inter boss during his media commitments.
The Spaniard, who is contracted to Madrid until 2016, has declined the opportunity to follow his former boss to west London but could leave during the off-season after new coach Carlo Ancelotti chose Zinedine Zidane as his assistant.