The Spanish midfielder is reportedly looking for a move away from the Bernabeu after making only seven appearances so far this season.
With the news of a possible departure, the 24-year-old's agent has revealed that there has been interest from Liverpool.
"He's finding his chances limited at Real," Teo Lazaro told The International Business Times.
"He's keen for a move away - possibly to Liverpool.
"If he can't play at Madrid then he'll play somewhere else. It's as simple as that."
Real Madrid exercised a buy-back option on Granero to bring him back to the club from Getafe in 2009.