The Argentina international has previously been linked with a number of Premier League clubs, and has now seemingly attracted the interest of Los Blancos
The Santiago Bernabeu side are in the market for reinforcements in the centre of the pitch as Lassana Diarra is expected to depart the club, and they supposedly see the 26-year-old as the perfect replacement.
The Argentina international joined Anderlecht from Independiente in the summer of 2006, and has since developed into a key player at the Brussels side, making over 150 league appearances for the Belgian giants.
Biglia signed a new contract until June 2015 at the start of this season, but he is believed to be keen to move to a bigger club in the summer transfer window.
The midfielder has previously been linked with Arsenal and Manchester United, but the Premier League side's interest seems to have cooled down a bit in recent months.