The playmaker has made 51 league appearances - netting 11 times - since joining the Madridistas in 2007.
However, following the expensive acquisitions of Kaka, Cristiano Ronaldo, Karim Benzema, Alvaro Arbeloa and Xabi Alonso, Real are open to offers for Dutch quintet Sneijder, Rafael van der Vaart, Arjen Robben, Roysten Drenthe and Ruud van Nistelrooy, while Klaas-Jan Huntelaar has already joined AC Milan.
Sneijder - who has been capped 52 times by his country - has been linked with moves to Chelsea, Arsenal, Tottenham Hotspur, Aston Villa and Inter Milan.
And it is the latter who are reportedly in pole position to snare his signing, despite the Nerazzurri struggling to meet Real's valuation of the player.
The Dutchman is currently on international duty with the Netherlands, who take on Fabio Capello's England in Amsterdam on Wednesday night.
However, according to La Gazzetta dello Sport, talks between Inter and Real are continuing in the player's absence.
And the San Siro giants are believed to be close to agreeing a €7 million deal to take Sneijder on loan for the season, with the option to make the move permanent for an added €13 million next summer.
NEWS: Inter in talks to sign Sneijder
NEWS: Villa reveal Sneijder appeal
NEWS: Sneijder switch to San Siro ruled out
NEWS: Sneijder eyes Real Madrid move
NEWS: Van der Vaart set for switch
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