The 24-year-old Spanish midfielder has been told he is surplus to requirements at the Bernabeu by Los Blancos boss Jose Mourinho, but is unwilling to let the former Getafe man leave the club on loan.
Reds boss Kenny Dalglish was recently credited with an interest in bringing Granero to Anfield as midfield cover for Lucas Leiva, who has been ruled out for the remainder of the 2011-12 campaign.
Add to that, Steven Gerrard's precarious fitness situation and Liverpool are a little short on central midfield options, and would be boosted by the addition of the Real star.
However, the Merseysiders face competition for the former Spanish U21 starlet's signature from relegation-threatened Blackburn, as Steve Kean looks to make an audacious transfer coup for his struggling side.
Madrid paid £4million for Granero back in 2009, and will demand double that fee from Blackburn and Liverpool if either club wishes to land him.