The defender is yet to agree a new deal and that has reportedly sparked interest from the Premier League duo.
The defender only has a year left on his contract at the Bernabeu and is yet to agree new terms, with recent negotiations having been halted by the club.
That means, as things stand, he is free to negotiate a deal with any other clubs interested in him come January, under the Bosman ruling, and the Premier League duo would apparently be more than keen to discuss a move to England with him.
According to the report, new Madrid manager Rafa Benitez is to put his faith in highly rated French youngster Rafael Varane meaning 32-year-old Pepe may have to play second fiddle at the club to him and Sergio Ramos.
An improvement for both sides
At both City and Chelsea though, he would likely play a starring role, despite his age. At the Etihad, the signing of Eliaquim Mangala has so far proven to be a mistake, while the likes of Martin Demichelis and Dedryck Boyata are yet to impress wholly either.
Jose Mourinho has better options at Stamford Bridge with John Terry and Gary Cahill proving a solid defensive duo last season and youngster Kurt Zouma performing well when called upon. However, Pepe would likely start ahead of Cahill if they were to compete for the one position and Zouma is not yet ready for a permanent starting role.
Indeed, given that Pepe and Mourinho previously worked well together at Madrid and are compatriots, a deal to join the Premier League champions seems more likely.