The 25 year-old has enjoyed an extremely good season and with his efforts, Bilbao have secured the all important 4th place and a shot at the Champions League next season after a poor season the year before.
With Real Madrid's efforts to sign one of either Paul Pogba or Arturo Vidal not going so well, a move for the Bilbao player could be on the cards as he is viewed as the alternative to the Juventus duo.
Real Madrid are not ruling out a move for the defensive midfielder who has a 36 million release clause in his contract meaning that they would it be very hard to get Iturraspe for a lesser fee.
Iturraspe has made 38 appearances in the La Liga and Copa Del Rey this season with 3 assists tallied throughout his campaign as well.