The Venezuela international is out of contract at the end of the season and he has failed to agree terms regarding an extension at San Mames.
Bilbao have withdrawn the offer of a new deal as a result and Amorebieta has reportedly been attracting interest from Arsenal and ambitious Russian club Anzhi Makhachkala.
However, it is understood that the centre-half's representatives are currently in Italy talking to clubs about a possible Bosman move in the summer.
Juventus, AC Milan and Inter Milan are all thought to be chasing the 27-year-old, who has made over 250 appearances for Bilbao.
Italian champions Juventus have already agreed a deal to sign Amorebieta's team-mate Fernando Llorente, with the striker also quitting Bilbao on a free transfer at the end of the season.