The west Londoners have been granted permission by the Spanish giants to speak to their out-of-favour midfielder, with only personal terms and a medical left to be completed
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The two clubs have settled on a fee, and all that remains is for Granero to agree personal terms and complete a medical ahead of a permanent switch to Loftus Road.
Ian Taylor, the Rs press officer, tweeted: "#QPR have reached agreement with Real Madrid for the permanent transfer of midfielder Esteban Granero ...
"The deal is subject to (Esteban) Granero agreeing personal terms and passing a medical."
Should the deal be completed, the Spaniard could become the 10th new arrival of a busy summer for QPR, who are looking to seal the signing of Stephane M'Bia from French giants Marseille.
Boss Mark Hughes is also believed to be interested in Granero's Real Madrid team-mate Ricardo Carvalho, who has been told by Jose Mourinho that he is not in Los Blancos' plans for this season.