The 23-year-old midfielder, who has struggled to settle at the Santiago Bernabeu since arriving from Borussia Dortmund last year, has previously been linked with Inter
The Turkey international only arrived at the Santiago Bernabeu last summer but struggled for form and fitness during his debut season in La Liga and there was even talk of him leaving the Spanish capital during the January transfer window.
Sahin has been heavily linked with Inter in recent weeks but, according to Sky Sport, Milan have now stolen a march on their city rivals, with Galliani having met with the player's representative, Reza Fazeli, on Wednesday.
The 23-year-old midfielder played a key role in Borussia Dortmund's 2010-11 title triumph and was voted the Bundesliga's player of the season.
As well as Inter and Milan, Sahin has also reportedly attracted the interest of newly-crowned Serie A champions Juventus.
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