The 39-year-old hailed his former colleague, saying it was a "privilege" to work with Jose Mourinho after Carlo Ancelotti was officially named as his successor last week
The newly appointed Chelsea boss endured a turbulent final year at Santiago Bernabeu, in which he had reportedly fallen out with a number of players towards the end of his three-year stay in the Spanish capital.
However, the 50-year-old seems to have retained the affections of his second-in-command at Madrid, who says it was a "privilege" to have worked with the Portuguese coach.
He 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.
Karanka, who is contracted to Madrid until 2016, has declined the opportunity to follow Mourinho to west London, but could leave during the off-season after new coach Carlo Ancelotti chose Zinedine Zidane as his assistant.