The newspaper reports Diaz has been identified as a loan replacement for Manuel Lanzini, who has been ruled out for the best part of a year with damaged cruciate ligaments.
The 18-year-old is said to have been earmarked as a future star at Manchester City, with Pellegrini's successor, Pep Guardiola, described as being a 'huge fan'.
But it is the new West Ham manager who brought Diaz to the Etihad Stadium from Malaga five years ago, having also worked with the Spaniard - as well as the Hammers' new head of recruitment, Mario Husillos - at La Rosaleda.
Diaz has only played 11 times for Manchester City do date, and could increase his game time with a move to West Ham.
The London side have also been linked with a move for another Blues starlet in Phil Foden.
Would West Ham be a good move for Diaz?