The Brazilian has been struggling with injuries during his spell at Anfield but Benitez is keen on keeping him at the club.
Aurelio’s current contract is set to expire at the end of the season.
Benitez said in the Sunday Mirror: “Fabio has been really unlucky. When we spoke to him about a contract extension he had an injury and he has had lots of injuries in the past.
“We made him an offer and his agent rejected it. Then he suffered another injury and we have had to analyse the situation again.
“We will talk again in the future because he is a good person, a great professional and a great player.
“Maybe his situation needs to be looked at in a different way and he needs to be realistic.”
