The Spanish side have been the biggest spenders in Europe this summer, capturing some highly-rated players such as Javier Pastore.
Now according to Spanish daily AS, the club are ready to launch a bid to prise Granero from the Santiago Bernabeu.
The 24-year-old has fallen down the pecking orders in Jose Mourinho's side and is desperate for more first-team football.
He could well be tempted by a move to Malaga as it could mean a reunion with Manuel Pellegrini, who coached Madrid for a season.
Pellegrini is believed to be interested in signing his former player, who enjoyed his best spell at the Bernabeu under his leadership.
Granero has played over 150 games for Madrid, scoring 19 goals.