How those talks developed will now play a huge bearing on his future, because the Gunners face serious competition for the 27-year-old.
Amorebieta is a Venezuelan international who plays for Spanish club Athletic Bilbao, who is out of contract this summer, so picking him up on a free would be a great piece of business for Arsenal.
However it has now been reported by Football Italia that three of Italy's biggest clubs are interested in signing him: Inter Milan, AC Milan, and Juventus.
Can Arsenal win the race? It depends how Arsene Wenger views the Venezuelan. Is he going to be first choice or fourth choice. How will this be communicated to the defender?
Amorebieta clearly allowed his contract to run down because he wanted to secure the best move possible for himself, and this means going to play first team football somewhere.
If Arsenal are not going to offer that to him, then it is likely he will plump for an alternative.
Aside from the fact Arsenal will need to secure Champions League football to offer Amorebieta the best package, Juventus also hold a trump card.
Not only are the Turin club top of Serie A by six points and practically have their own qualification confirmed, and can offer Amorebieta chances of winning medals; they are also the club where his teammate Fernando Llorente is heading in the summer.
Amorebieta could be tempted to follow Llorente, and if he did, it will be an outstanding pair of deals pulled off by Juventus, who are on the lookout for a new centre-back after their signing of Lucio last summer turned out to be a bust as he got injured and was later released.
Inter and AC will be able to tempt Amorebieta too, so if Arsenal are serious and want him to play a key part next season, they need to step up their negotiations now.
Is Amorebieta of use to Arsenal next season and can they pull it off?
image: © aalarcon