Granero had been linked with a move to Anfield in January but his representatives have denied that Granero is unhappy at the Bernabeu.
"Granero is going to continue with Real Madrid, 100%," a source told IB Times UK.
"He played 65 minutes in the last match in the Bernabeu against Athletic Bilbao and maybe the coach is going to consider him more for the future."
Granero has found it difficult to break into Jose Mourinho's team this season due to the high number of midfielders at the club.
Real Madrid are currently first in La Liga.