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, reports have suggested that 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 himself - 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, coached by former Chelsea supremo Jose Mourinho, who have made their move to land the midfielder, after the player's representitive, Soren Lerby, confirmed he had held talks with the Italians.
"For some time there has been talk of a move for Sneijder to Inter, but the reality is that anyone who wants to buy him must simply satisfy the demands of the club," he told 24oredisport.
"Sneijder definitely wants a club that can guarantee his constant use.
"A few days ago I spoke with someone from Inter, but the problem is the money required by Real. The possibility he remains in Madrid is still quite high."
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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