The Nerazzuri's Argentine international is set to go under the knife after injuring his knee during a friendly against Juventus.
And, according to Il Corriere Dello Sport, San Siro boss Jose Mourinho is now ready to recruit Sneijder as a replacement for his stricken midfielder.
The playmaker has made 52 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 53 times by his country - has been linked with moves to Chelsea, Arsenal, Tottenham Hotspur and Aston Villa, as well as Inter.
Recent reports have suggested that the latter are 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.
And although the Dutchman has made no secret of his desire to remain with the 31-time la Liga winners this season, he has admitted he would be attracted by a move to Milan should he decide that his future lies away from Spain, saying:
"I have heard that Mourinho considers me his first choice.
"He is a great coach that trains a great team. If I decide to leave Madrid, Inter would be a nice option."
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