The Hammers have lost Lanzini for up to nine-months â€“ a large part of next season â€“ after he suffered cruciate knee ligament damage.
And Pellegrini wants to take Diaz as the Argentine's replacement for the coming campaign, with City knowing he needs regular playing time.
A source told The Sun: â€œManuel is a huge admirer of Brahim and would like to take him following the horrible injury to Lanzini.
â€œHe is one of the brightest talents in the City academy. He needs more game time and Manuel is well aware of that."