The 30-year-old joined Liverpool on a free transfer from Valencia in 2006.
Aurelio’s contract with Liverpool expires this summer and the Brazilian defender can leave the club on a free transfer.
“Fabio’s contract is nearly finished and he is going to leave us,” Benitez told the club’s official website.
“We had been trying to work something out with regards an extension but it was a pity that we couldn’t.
“Fabio is a top professional, a great player and a really good lad. I mean every single word I say about him.
“It has been a pleasure having him here and we really will miss him.”
“The one problem we had with Fabio was that he suffered too many injuries and it was such a pity because he has great quality,” he continued.
“When he was in the team, we were always able to play the ball out from the back and keep it because he uses possession so well.
“With Fabio being out so much, it meant that we had to use Emiliano Insua more than we would have liked and that was not easy for him.
“You can say things about players. But with Fabio, you are talking about an amazing person who gave 100 per cent all the time. We wish him all the best.”
