The Germany international midfielder joined the Spanish giants on a six-year deal back in July, ending a seven-year association with Bayern.
"I'm happy to have been given the chance to try something new. Even though it's only been a short while I fell like it was the right decision," he told Die Welt. "Madrid is a special club and the challenge I was looking for after my long and successful career at Bayern."
Kroos has made 12 appearances in all competitions for Madrid so far this season.