Inter president Massimo Moratti confirmed accepting a reported 10million euro bid for the unsettled Holland international after Galatasaray made their approach public on Tuesday.
Sneijder has cut an isolated figure at the San Siro this season, making just five league appearances and publicly refusing to accept a two million euro wage cut.
Turkish Superlig leaders Galatasaray are enjoying a three-week winter break but are eager to add Sneijder to their ranks before next week's trip to Kasimpasa.
Quoted in the Gazzetta dello Sport, Galatasaray director of sport Bulent Tulun told Turkish radio station Radyospor: "Sneijder will give us a response inside 24 hours, but in 99 per cent of these cases the transfer negotiations are already done."
Moratti broke the Serie A club's silence, confirming Inter were prepared to sell the man they signed from Real Madrid for 15million euros in 2009.
"Galatasaray's offer satisfies us. Now it depends on the player," Moratti told Sky Sports. "We would be happy if he decided to stay on our terms."
Sneijder has reportedly attracted the interest of Manchester United, Manchester City, Liverpool and Tottenham, as well as ambitious Ligue 1 outfit Paris Saint Germain.
But unless a late counter-offer is made, the 28-year-old could end his three-and-a-half year association with Inter to become a Galatasaray player before the weekend.