The Liga giants decided to cash in on the much-loved attacking midfielder in a £42 million move to Arsenal following the arrivals of Isco and Gareth Bale at the Santiago Bernabeu
Los Blancos pocketed £42 million from the sale of the 24-year-old playmaker, whom they signed from Werder Bremen for a reported €15m [£12m] in 2010.
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"I knew that Mesut was feeling very comfortable at Madrid," the Germany international said in an interview with Bild. "But, in football, things can happen quickly.
"Real threw everything overboard [this summer] - new coach [Carlo Ancelotti], new stars [Isco, Gareth Bale]. I wouldn't have sold Mesut.
"However, I had the feeling that he is looking forward to a new chapter in his career at Arsenal."
Meanwhile, Muller says that he has no desire to leave his current club, Bayern Munich, admitting that he is enjoying playing under new boss Pep Guardiola as much as he does Germany coach Joachim Low.
"He has a lot of fun with his work," the 23-year-old enthused. "His goal is to positively influence the outcome of a football match.
"He makes great speeches and on the sidelines; he is similarly emotional as Jogi Low."