The defender was on loan at Middlesbrough for much of last season, and is desperate to leave Craven Cottage.
The 31-year-old moved to Craven Cottage from Athletic Bilbao in 2013, featuring as Fulham were relegated from the Premier League after 13 seasons. He played 26 times in the English top flight, and since relegation initially turned out rarely in West London, with much of his football instead coming during two loan spells at Middlesbrough, the latest of which saw him play in 13 matches at the Riverside.
Fulham's Fernando Amorebieta celebrates scoring their second goal
He returned to Fulham in February though, and started 14 out of the Cottagers' final 18 matches under Slavisa Jokanovic, helping them edge to safety with a 20th place finish.
Amorebieta, who has 15 international caps to his name, was not selected for this summer's Copa America, with the defender retiring from international duty after last year's tournament, which saw the powerful defender sent off against Peru for a stamp on Paulo Guerrero.
Fernando Amorebieta celebrates after scoring the second goal for Middlesbrough
There is currently no reported interest in Amorebieta, with Middlesbrough not credited with as following the player as they prepare life back in the Premier League. His contract expires at the end of the coming season, but he has plenty of experience, with nearly 200 La Liga appearances at boyhood club Athletic.
Given the player's wishes, Jokanovic may be eager to move on a player who will still be on Premier League wages, freeing up finances for the Serb to use elsewhere in the squad.
Brighton’s Bruno and Fulham’s Fernando Amorebieta in action