However, the Spain captain admits Gala won't be his last club with ambitions to return to LaLiga.
The former Atletico Madrid striker told Marca: "We want the fifth star on the shirt, which is Galatasaray's 25th victory in the Turkish championship.
"I am very happy in Istanbul. I am living an experience that at first glance may seem different, but I have found a wonderful country, an incredible club and extremely nice people. I love the life I lead here and I am very happy to have come.
"If everything goes well, next season I will play in the Champions League and that is an important thing for me. I wanted to continue competing at the highest European level, which is not easy."
Asked about unfulfilled ambitions, Morata also stated: "I will not talk about dreams anymore, even though I dreamed of playing for Galatasaray... I'm joking.
"I would like to reciprocate the esteem and affection that the president of Getafe, Ángel Torres, showed me when I was 13. My heart asks to go back there and enjoy a year or two, or whatever it will be. I hope to be able to do so after this experience in Turkey. Maybe there will not be a place for me, I don't know, but I would love to play for Getafe and end my career."