The 29-year-old has been touted as a possible transfer target for José Mourinho after the Portuguese coach returned to the Stamford Bridge helm on a four-year deal earlier this month.
Galatasaray claimed that they would listen to offers of around £12.75m for Sneijder last week.
But Sneijder, who won an historic treble at Inter Milan under Mourinho, says that he plans to stay at the Turkish club.
“I moved here for a new culture and to get to know a new culture, and I can’t forget that,” said Sneijder.
“I have a good relationship with Mourinho and enjoyed working with them, but I love Istanbul and I owe a lot to Galatasaray.”