Inter president Massimo Moratti is willing to allow the unsettled Dutch midfielder to leave but any deal will depend upon the Turkish club reaching an agreement with the player.
"Galatasaray's offer satisfies us. Now it depends on the player," Moratti told Sky Italia.
"We would be happy if he decided to stay on our terms."
Sneijder has reportedly been asked to accept a two million euro pay cut to his annual salary with the Nerazzurri.
But Inter head coach Andrea Stramaccioni continues to maintain that the 28-year-old's absence from the first team is purely a tactical decision.
Sneijder is believed to be holding out for better offers from a host of Premier League clubs as well as big-spending Ligue 1 outfit Paris St Germain.
On Wednesday, Sneijder's agent, Soren Lerby, refused to confirm Gala's claims that they had opened talks, telling De Telegraaf: "Every day there is a new club linked with Wesley.
"For that reason I have decided not to answer any more questions."
But a statement on the Turkish club's official website read: "Galatasaray announces it has begun negotiations with FC Internazionale for the transfer of Wesley Sneijder.
"The public will be informed of developments."