Pepe has said he will discuss his future at Real Madrid with president Florentino Perez but insists he loves the club and is willing to honour his contract.
The Portugal international has attracted interest from Manchester City, who are looking to sign another central defender.
However, City accept it will be hard to recruit Pepe after Madrid’s new coach Carlo Ancelotti, reportedly said last month that he wants to keep the 30-year-old.
Pepe has stopped short of guaranteeing he will be at the Bernabeu again for the forthcoming season, with Sergio Ramos and Raphael Varane expected to be the club’s first-choice centre-backs.
Speaking after Madrid’s 2-1 win over Everton in a pre-season encounter in Los Angeles, the former Porto player admitted he is not certain whether he will remain in Spain.
"I'm a professional," he said. "They left a lot of things unsaid at the end of last season but I have a contract to fulfil.
"I'm talking to the president of Madrid and my representatives to see what will happen. I have a contract, I love the club and I have great affection for the people.”
Pepe joined Madrid from Porto in 2007 and has made 199 appearances for the club since then.
City lost one central defender this summer when Kolo Toure joined Liverpool, while Matija Nastasic picked up an injury while playing in the Barclays Asia Trophy last month.