The Turkish club confirmed on Tuesday they have entered negotiations with Inter over a reported 10million euro deal for the 28-year-old, who has not played for the Nerazzurri since September.
Sneijder has publicly rejected the possibility of accepting a two million euro pay cut to his annual salary at the San Siro, but Inter head coach Andrea Stramaccioni maintains the Holland international's continued absence from his first team is solely a tactical decision.
When questioned about any potential switch to Istanbul, Sneijder's agent, Soren Lerby, told De Telegraaf: "Every day there is a new club linked with Wesley. For that reason I have decided not to answer any more questions."
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 on Tuesday Galatasaray became the first club to publicly confirm making an approach.
A statement on the Turkish club's official website, galatasaray.org, read: "Galatasaray announces it has begun negotiations with FC Internazionale for the transfer of Wesley Sneijder. The public will be informed of developments."
Sneijder joined Inter in August 2009 after winning the Primera Division with Real Madrid during a two-season stint in Spain, going on to claim the Champions League trophy, Serie A title and Coppa Italia at the first time of asking before reaching the World Cup final with Holland, only to lose out to Spain.
However, the departure of Inter head coach Jose Mourinho in 2010 saw Sneijder's importance in the team steadily diminish under subsequent coaches, despite the fact he had signed a five-year contract in the summer, and the ex-Ajax man has only made five league appearances under current boss Stramaccioni this season.