The 23-year-old defensive midfielder won rave reviews for his performances in Germany's successful World Cup finals this summer.
Only last week Stuttgart quashed reports Khedira could be set to join the Spanish giants, but now they have officially changed their position.
With Khedira now in the final year of his contract Schneider has hinted a deal could be brokered rather than losing him for free next summer.
"Months ago we have tried to thrash out a contract extension with (Khedira), we did not succeed," Schneider told kicker-Sportmagazin.
"And now Real Madrid has officially indicated their interest in him."