Pepe is out of contract at the end of the season
The Euro 2016 winner, 34, is out of contract at the end of the season.
Pepe is represented by super-agent Jorge Mendes, who has been tasked with trying to sort out a two-year deal for his client.
So far a contract hasn't been forthcoming but the Portuguese defender has now reiterated his desire to stay at the Bernabeu.
He said: "I have already said, I will wait for Madrid until the last second, I sacrifice every day to be here.
"For me it is a great honour to be here.
Pepe wants to sign a two-year deal to stay at Real Madrid
"I want [the fans] to be very happy because I have always tried to honour this shirt, learning from guys like Raul, showing team spirit and respecting those at the stadium.
"I always want to give my utmost to try and bring happiness to the supporters.
"Only God knows what my future holds because I have a contract until June 30. I am just focusing on returning as soon as possible to help the team.
"We are going to give it our all for the rest of the season to win all of the competitions we are in."
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Pepe was speaking at a supporters' event alongside Real legend Raul.
He's desperate for Pepe to stay and said: "I've been through a lot with Pepe, we have shared things on and off the pitch and I wish you the best in the world.
"I would like to still see you wearing the Madrid shirt, hopefully you can stay."