The Dutch playmaker has been linked with a summer move to Stamford Bridge to be reunited with former manager Jose Mourinho.
Sneijder worked with the Portuguese coach during a successful spell at Inter Milan.
"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," the 29-year-old told Milliyet.
"I want to play till January at least and help my team. I love Istanbul so much."
Sneijder's current contract with Turkish champions Galatasaray is due to expire in the summer of 2016.