The 30-year-old Portugal international has fallen out of favour at the Bernabeu, with teenage French defender Raphael Varane preferred as Sergio Ramos's partner at the heart of the Real Madrid defence.
But the report claims Madrid still value Pepe at £20m - a figure which could put City off considering the defender's age.
Pellegrini has been tipped to replace the departed Roberto Mancini in the City hot-seat this summer, although nothing has been confirmed as yet.
The Chilean must solve a number of awkward problems should he take the reins, with Carlos Tevez the latest to be linked with a summer exit.
The Argentinian forward has reportedly admitted he'd be keen to move to Paris St Germain this summer. The newly crowned Ligue 1 champions almost signed Tevez last year, and he's revealed he would be open to another offer.
Up to 12 Manchester City first-team players have been linked with moves away from the Etihad Stadium this summer, in what could be a transformational three months for the 2011/12 Premier League champions.
Mancini clearly felt he was hampered by an inability to conduct his transfer business early in the summer, and City look keen to avoid the same mistake this term - abet with the Italian boss no longer at the helm.
Pepe would join the squad and challenge Vincent Kompany and Matija Nastasic for a starting berth. The young Serbian defender successfully ousted Joleon Lescott for the starting XI this season.