Liverpool were said to have considered signing the Blancos' youth academy product, who will be out of contract next year, during the January transfer window
According to MARCA, a Premier League club submitted a sizeable bid for the 25-year-old Madrid native, who made just 17 appearances in last season's Liga-winning campaign.
However, even though Granero only has a year to run on his current contract with Los Blancos, the offer was rejected because Jose Mourinho views the player as a valuable member of his squad.
The youth academy product was heavily linked with a move to Liverpool during the January transfer window but the Reds' rumoured interest never materialised into a formal approach.
Granero, who was capped by Spain at Under-21 level, spent two seasons on loan at Getafe before returning to the Santiago Bernabeu in 2009.