The Germany midfielder looks certain now to part ways with Bayern Munich, with only contract details to agree with the Spanish club this summer.
The Germany star, 24, was pivotal in Joachim Low's World Cup-winning team this summer and Castrol's FIFA index suggested he was the best player in the tournament.
His performances in Brazil - and for Bundesliga champion Bayern over the past couple of seasons - have landed him firmly on Real Madrid's radar and Carlo Ancelotti looks close to securing his first big transfer coup of the summer.
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"Tomorrow or in the next few days I will go to Real Madrid," Kroos told AS while holidaying in Majorca.
He added, when asked how his mood was following Germany's heroics in Brazil: "Of course I'm delighted right now, how could I not be after winning the World Cup?!"
Bayern CEO Karl-Heinz Rummenigge had already paved the way for Kroos' exit by suggesting that the Bavarians would cash in on the midfielder for the right price.
Kroos, who has been with Bayern since 2006, looks set to head into a Blancos midfield which currently includes Xabi Alonso, Asier Illarramendi, Sami Khedira, Angel Di Maria, Luka Modric and Casemiro.