Benitez is keen to keep the Spain shot-stopper on Merseyside.
He told the club’s official website: “Everyone knows he’s a good goalkeeper who has kept a lot of clean sheets for us and broken good records.
“He’s someone who has a very good mentality who helps team spirit. He’s a very important player for us, and one of those player who everyone can see is key.
“Pepe is one of the players who I will be really pleased if we can keep him for a long time.
“He is someone who is keen to learn, he wants to improve and is still young. He can be a top keeper for 10 more years; he has a great future and we’ve spoken to his agent to try and arrange something.
“He still has time on his contract but we are trying to keep him happy for the future, too. I have spoken with him and his agent. We have agreed that we have got to have a proper conversation in a few weeks.”
