The 29-year-old moved to the Istanbul-based outfit in January 2013, scoring three goals as Galatasaray claimed the Super Lig title.
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“I have a special relationship with Jose Mourinho and enjoyed working with him, but I can't leave Galatasaray in the lurch or the fans that I admire,” Sneijder told Turkish newspaper Milliyet.
“I want to play till January at least and help my team. I love Istanbul so much.”
Sneijder cost Galatasaray a fee in the region of £6.3 million, and the former Ajax and Real Madrid star feels he has an obligation to remain with the club.
“I've met a new country and a new culture. It would not be easy to leave and turn my back [on Galatasaray]," he continued.
“My club have expectations of me. The board worked so hard for my transfer. I can't go anywhere because I owe them.”