Sneijder's performances for the Netherlands during this summer's World Cup were thought to have attracted interest from a number of clubs across Europe.
But Galatasaray, who appointed former Italy manager Cesare Prandelli as head coach in place of Roberto Mancini last month, insist the Dutchman's future remains in Istanbul.
"Sneijder is going to stay with Galatasaray," Gala president Aysal was quoted as saying by Turkish media on Tuesday.
"It's not just our opinion but that of Cesare Prandelli and the player. There can be no talk of a split between us.
"He had a tiring season and right afterwards he played at the World Cup. He will rejoin us after the holidays."
Sneijder - a UEFA Champions League winner under Jose Mourinho at Inter Milan in 2010 - is understood to have a 20million euro release clause in his contract and has been linked with Manchester United and Chelsea.
Monaco are also thought to have earmarked the 30-year-old as a replacement for James Rodriguez, who joined Real Madrid earlier this month, but a move to Ligue 1 was dismissed by Sneijder's agent Guido Albers.