The Netherlands international could be on his way out of San Siro after Massimo Moratti gave the green light to a move to Turkey, with the switch now in the hands of the player
The midfielder has been firmly out of the first team picture since since September, after rejecting reduced terms on a new deal.
The Istanbul club are the first side to have a bid accepted, but representatives of the former Real Madrid playmaker have yet to comment on Sneijder's potential interest in a move to Turkey.
"Galatasaray's offer for Sneijder has arrived and we are happy with it, so now it all depends on Wesley," Moratti revealed on Wednesday.
"I haven't yet spoken to him. If he were to remain under our conditions, then he would be a great help."
Formal negotiations began on Tuesday and it is reported the Netherlands international has been offered a €6m (£4.9m) per season wage package to make the move to the Turk Telekom Arena.