Sneijder - who has been capped 53 times by his country - has also been linked with Chelsea, Arsenal, Tottenham Hotspur and Aston Villa.
But with Inter having lost Argentine enforcer Esteban Cambiasso through injury, Inter are keen to land a suitable replacement as soon as possible.
Real general director Jorge Valdano was believed to have flown to Germany on Wednesday - where Madrid were playing Borussia Dortmund in a friendly - to speak face to face with Sneijder about a move to the San Siro.
The Dutchman took no part in the Spaniards' easy 5-0 win.
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