La Real have been keeping close tabs on the player for quite a while now, but they finally appear ready to step up their interest.
After his proposed transfer to CSKA Moscow fell through, Suarez is again available for sale, while he has finally recovered from a serious knee injury.
Real Sociedad have launched an official enquiry into the player’s availability and have been told they can sign him for €9 million.
With La Real having qualified for the Champions League through league finish, the Argentine should be well within their price range.
Matias Suarez, 25, joined Anderlecht in 2008 from Belgrano and has since scored 35 goals in 126 league games for the Belgian giants.
Following a lengthy spell on the sidelines, the Argentine returned into action in March, featuring in 11 league matches last term and scoring 3 goals.