The 33-year-old centre-back just completed his ninth campaign with Real, helping the team clinch the Champions League trophy after finishing runners-up to Barcelona in La Liga.
"I hope this is not my last year at Madrid," Pepe told Marca. "I look after myself a lot to be at the top of my game for as long as possible.
"I have one more year left and I hope that through my performances the club will offer me one more year or perhaps two. I will always give priority to Madrid.
Pepe dropped down the pecking order after Rafa Benitez took over as manager last year but under Zinedine Zidane the Portugal international got more opportunities.
"Benitez is a very good professional," Pepe said. "I really liked the way he worked but he was unlucky. He was very honest with me and told me that I would not be his first choice but I told him to let me work in case I was given a chance.
"I have been 10 years at Madrid, which is no easy thing."
Pepe is the longest-serving Real player after captain Sergio Ramos and Marcelo.
He finished the campaign with 31 appearances in all competitions and started in Real's Champions League final victory against Atletico Madrid.
"It has been a personal victory," Pepe said. "In the end hard work pays off. I have won two Champions League trophies and I have entered the history books of Madrid."
Pepe has been included in Portugal's squad for Euro 2016.
(Reporting by Adriana Garcia, editing by Ed Osmond)
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