Having joined the Spanish giants from Porto in 2007, Pepe played under Manuel Pellegrini during his year in charge at the Bernabeu.
The new Blues boss said before Saturday’s pre-season match with Sunderland that while his squad is not yet complete, it’s “very near”.
Kolo Toure has left to join Liverpool this summer and although Pellegrini is yet to sign a defender this summer, he is believed to have targetted Pepe, 30, who is rated at £15m (Source: Sunday Express) .
Fellow centre-half Joleon Lescott has also been linked with a move away from the Etihad this summer while Matija Nastasic was injured during the Sunderland game.
Left-back Aleksandar Kolarov is another defender expected to leave City this summer, with Galatasaray making a £4m bid for the Serbian (Daily Star Sunday) .
Juventus had offered a £1.5m fee to loan Kolarov for the season but the Blues are willing to let the 27-year-old leave on a permanent basis.
Galatasaray’s initial offer has been turned down, though, with City hoping for a £6m fee.