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The Brazil international ended his nine-year stay at the Santiago Bernabeu when he swapped LaLiga for the Premier League earlier this month for a reported fee of £60million (€70m).
Casemiro, who made his United debut as a substitute during Saturday's 1-0 win at Southampton, enjoyed a trophy-laden stint alongside Kroos in the heart of Los Blancos' midfield.
Together, they won four Champions League crowns and two league titles, and the 30-year-old's decision to leave the Spanish capital was one that came out of the blue, according to Kroos.
Speaking on his podcast Einfach mal Luppen, Kroos said: "The decision surprised me to do that. He has made the decision for himself to do something new again.
"He's 30 and knows for sure that he won't need to do that in two or three years. There were more and more reports, it somehow got hotter.
"In the beginning, I would not have expected it at all, I thought it was just a rumour at first. But there are one or two newspapers here that are a bit better informed.
"As more and more people reported and talked about details, I was awake at three or four o'clock at night when I was sick. Then I just wrote to him [asking] if he would really leave me alone."