Recently installed City boss Manuel Pellegrini worked with the Portuguese player during his time in charge of Real, and is looking to bring in more new faces to his squad.
Real supremo Florentino Perez claimed Pepe was not for sale in July, and Pellegrini would not be drawn when asked about the 30-year-old on City's recent pre-season visit to Hong Kong.
Former City captain Kolo Toure left the 2012 Premier League champions for Liverpool when his contract expired this summer, and with England international Joleon Lescott entering the final year of his deal at City, another defender could be on Pellegrini's wish-list.
But speaking after Real's pre-season friendly with Everton in Los Angeles, Pepe was guarded when asked about a possible move away from the Bernabeu.
"I'm a professional. They left a lot of things at the end of last season but I have a contract to fulfil," said Pepe, who played in both Real Madrid v Man City matches in last season's Champions League.
"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."