Karl, 18, has previously spoken about his admiration for the Spanish giants and is represented by Ballack, who played for Bayern during his career.
Speaking on the Kerners11 podcast, Ballack said the teenager's comments had been taken out of context.
“They asked him, ‘Which is your favourite club apart from FC Bayern?’ That part tends to be omitted. There was actually nothing wrong with what he said.”
Ballack explained that Karl was simply discussing an ambition he might like to fulfil later in his career.
“He was simply talking about a dream that perhaps one day he would like to fulfil by playing for Real Madrid. I also always had that in the back of my mind,” Ballack said with a laugh.
Karl remains a Bayern Munich player and is regarded as one of the club's promising young talents, but his comments have inevitably fuelled speculation about his long-term ambitions.
Ballack's explanation suggests the Real Madrid remarks were about a personal dream rather than an indication that Karl is actively seeking a move away from Munich.